I've just spent a couple of hours going through and looking at all the religions in teh game, trying to figure out their strengths and weaknesses. Since there doesn't seem to be any guide online for that, I thought it might be useful if I put the notes I made up on the forum to save other people some time.
For future reference, this is based on v42 of the game. And I'm definitely not an expert, so there's probably stuff that I missed. When I talk about "basic" or "standard" buildings, I mean the equivalent of the temple/monastery/cathedral arrangement from the vanilla game. Not all religions have these, but most do. It should be mentioned that at the time of writing, most religions' cathedrals aren't capped based on the number of temples you've made, but you can only build them in settlements with a City Council, which requires Refined culture.
Comments are welcome!
Andeanism
Era: Ancient
Lots of science bonuses from all the religious buildings. Holy city building gives gold. Two extra world wonders: El Dorado gives a bunch of gold, and Machu Picchu makes mountains workable.
Asatru
Era: Classical
Basic buildings give bonus XP for melee units. Holy city building gives gold, and more XP for melee units. Four world wonders, giving extra population, defence, reducing the whipping penalty, and reduced war weariness and a bonus promotion for melee units. Seeing a pattern here?
Baha'i
Era: Industrial
Basic buildings give a minor science bonus. Holy city building makes all the basic religious buildings give more science. Has one world wonder, which upgrades all the AI attitudes to cautious at worst.
Buddhism
Era: Classical
Bit of a generalist. Basic buildings are pretty standard. Holy city building gives gold and a good amount of culture. Has four world wonders giving different things. Also has some wonders and buildings which are shared with Hinduism, Confucianism and/or Taoism. Offers three separate national beliefs which help with crime.
Canaanism
Era: Ancient
Doesn't give very much, to be frank. Basic religious buildings are pretty standard. Holy city building gets gold. There's not really anything going for this religion, as far as I can see. More fodder for an extra religion if you're spiritual than a good choice for a state religion.
Cao Dai
Era: Atomic
Another religion with nothing special about it. To add insult to injury, the monastery goes obsolete soon after you found the religion, and you can only build cathedrals in half your cities. Holy city building gives health to all cities on its continent, and doesn't reward spreading Cao Dai.
Christianity
Era: Medieval (shouldn't this be Classical?)
Basic religious buildings are standard, but there's an extra one: the citadel, which gives big defensive bonuses, xp to siege weapons and an extra trade route. There's also an extra building you can make once you reach the renaissance, which doesn't require Christianity to be the state religion and gives several minor bonuses. Holy city building gives gold. Three world wonders: the King's Crusade spawns crusaders and speeds up great generals, St Mark's Basilica gives a permanent bonus to all water plots, and the Holy See Library gives science and espionage.
Confucianism
Era: Classical
Basic stuff is mostly standard, but give a minor bonus to science and gold. Holy city building gives a bonus to troops. Two wonders, both focussed on science.
Druidic Traditions
Era: Prehistoric
Together with Shamanism, the earliest religion you can found. Rather than the usual temple/monastery/cathedral configuration, you get three tiers of building. Only half your cities can have the tier 2 one, and only a quarter can have the tier 3 one; but on the bright side you can build everything straight away and the later ones give free promotions. You can build addons giving you +2% food for each vegetarian bonus resource in the city's vicinity. Shamanism and Druidic Traditions are founded off the same technology, so if you found one you can probably found the other if you want.
Hellenism
Era: Classical
Monastery gives more science than usual. Cathedral gives less happiness, but this is more than compensated for by the Odeon, an extra building giving happiness and education. Monastery also gives out a promotion to units built in the city, giving a decreased upgrade cost and a bit of strength. Holy city building gives science, and gives enemies war weariness. Has four wonders, giving a mix of bonuses.
Hinduism
Era: Ancient
Standard religious buildings. Extra buildings giving tiny amounts of culture for cows and elephants, and a small science building if you have caste system. Can build three national beliefs that help with crime, like Buddhism. Has some wonders and buildings which are shared with Buddhism. Holy city building gives gold. Has two separate wonders which reduce whipping anger by 50% each as well as giving other bonuses, and a third giving happiness throughout your empire.
Islam
Era: Medieval
Gives more happiness than usual for being a state religion. Holy city building gives gold. Has an extra building giving 1 science. 4 world wonders, mostly giving trade.
Jainism
Era: Classical
Basic religious buildings give extra gold, but reduce military production. Holy city building gives gold.
Judaism
Era: Ancient
Basic religious buildings give health bonuses. Holy city building gives a lot of gold. Three wonders: Solomon's Temple gives science, the Masada buffs priests, and the Ark of the Covenant both buffs priests and gives a ton of happiness.
Kemetism
Era: Ancient
Basic temple gives an extra gold. Has two extra buildings to make culture, and holy city building makes culture and gives all specialists in all cities an extra culture. Two world wonders, giving schools of scribes in every city and bonus science, respectively. Also has three national wonders, which give culture in all cities and various other benefits.
Mesopotamianism
Era: Ancient
Instead of the usual temple/monastery/cathedral, this has 5 religious buildings. Each gives a promotion to various classes of pre-gunpowder units. There are also expansions giving bonus food from carbohydrates in the city vicinity. Holy city building gives gold and culture. Has 3 wonders, giving free courthouses, contact with civs on the same continent, and military bonuses.
Mormon
Era: Industrial
Lacks a cathedral, but gets a similar building which can be built alongside the temple. The monastery equivalent is a national wonder, but doesn't go obsolete so you can keep sending out missionaries. Holy city building gives a big bonus to gold and science based on how many cities have the religion.
Naghualism
Era: Classical
Basic religious buildings give gold, culture and espionage. If you manage to snag an Native American culture, the religion also unlocks the Ball Court which gives happiness, gold, culture and xp. Holy city building gives gold and culture, and free specialists for each mining/quarrying resource in the vicinity. Has four world wonders, mostly based around sacrificing people.
Ngaiism
Era: Ancient
Has an odd arrangement of buildings. The base temple allows you to make missionaries and gives the usual temple benefits. Two other buildings give combat promotions, and the final one gives almost nothing by itself but can be further upgraded to give big food and hammer bonuses from cows, sheep and pigs in the vicinity. Holy city building only gives culture.
Rodnovera
Era: Classical
Temple gives an extra gold. Otherwise pretty bare bones. Holy city building gives gold.
Scientology
Era: Atomic
Virtually no culture, happiness or science, but generates lots of gold instead. The holy city building, surprisingly enough, gives you lots more gold.
Shamanism
Era: Prehistoric
Very much a parallel of Druidic Traditions; pretty much the only difference is that the addons give you +5% food for each meat-based bonus resource instead of vegetarian ones. Shamanism and Druidic Traditions are founded off the same technology, so if you found one you can probably found the other if you want.
Shinto
Era: Ancient
Exchanges most of the usual happiness and science buildings for maintenance reduction and military bonuses. Holy city building gives gold and culture. Two world wonders, improving water plots and pillaging respectively.
Sikhism
Era: Renaissance
No monastery. (Missionaries can still be built, though.) Temple and cathedral give +1xp to archers, melee and gunpowder units. Holy city building gives gold. The basic benefits of the religion are also relatively good, giving small bonuses to gold, science and culture.
Taoism
Era: Classical
Fairly generic temple/cathedral/monastery, although the monastery gives a the martial arts promotion to melee and recon units. Holy city building gives gold. Three world wonders, all of which give benefits in all cities.
Tengriism
Era: Prehistoric
Doesn't have a monastery or cathedral. The basic temple building gives +15% military production, and there are several upgrades you can build which give combat bonuses to mounted units. You can also build horse trainers in all your cities provided you have a single horse. Holy city building gives gold and culture.
Voodoo
Era: Medieval
Can only be spread by missionaries. The basic temple is weaker than usual, giving up most of its usual benefits for a minor decrease in unhappiness from sacrificing population. The cathedral gives extra production and gold, and the monastery gives production and commerce instead of its usual science bonus. The holy city building gives gold, and the single wonder allows you to make the rather powerful Hellsmouth dog units. The monastery also allows you to make an improved worker.
Yoruba
Era: Ancient
This religion has five buildings: a basic temple, and four upgrades. Uniquely the upgrades can be built in any city with Yoruba in it, not just the one where you built the original temple. The base temple is nothing to speak of, but the upgrades give a significant food, hammer and commerce bonus from seafood and deer, a great people birth rate increase, a reduction in maintenance and a small bonus to military production. Holy city building gives gold.
Zoroastrianism
Era: Ancient
Zoroastrianism offers above average happiness if you choose it as your state religion, especially in cities with a sky burial tradition. The holy city building gives gold, and also gives culture in all cities. There are four wonders, all giving benefits that will help a larger empire. Zoroastrianism dislikes slavery, so you'll get a bunch of unhappiness if you have zoroastrians in your empire and are running that worldview.
For future reference, this is based on v42 of the game. And I'm definitely not an expert, so there's probably stuff that I missed. When I talk about "basic" or "standard" buildings, I mean the equivalent of the temple/monastery/cathedral arrangement from the vanilla game. Not all religions have these, but most do. It should be mentioned that at the time of writing, most religions' cathedrals aren't capped based on the number of temples you've made, but you can only build them in settlements with a City Council, which requires Refined culture.
Comments are welcome!
Andeanism
Era: Ancient
Lots of science bonuses from all the religious buildings. Holy city building gives gold. Two extra world wonders: El Dorado gives a bunch of gold, and Machu Picchu makes mountains workable.
Asatru
Era: Classical
Basic buildings give bonus XP for melee units. Holy city building gives gold, and more XP for melee units. Four world wonders, giving extra population, defence, reducing the whipping penalty, and reduced war weariness and a bonus promotion for melee units. Seeing a pattern here?
Baha'i
Era: Industrial
Basic buildings give a minor science bonus. Holy city building makes all the basic religious buildings give more science. Has one world wonder, which upgrades all the AI attitudes to cautious at worst.
Buddhism
Era: Classical
Bit of a generalist. Basic buildings are pretty standard. Holy city building gives gold and a good amount of culture. Has four world wonders giving different things. Also has some wonders and buildings which are shared with Hinduism, Confucianism and/or Taoism. Offers three separate national beliefs which help with crime.
Canaanism
Era: Ancient
Doesn't give very much, to be frank. Basic religious buildings are pretty standard. Holy city building gets gold. There's not really anything going for this religion, as far as I can see. More fodder for an extra religion if you're spiritual than a good choice for a state religion.
Cao Dai
Era: Atomic
Another religion with nothing special about it. To add insult to injury, the monastery goes obsolete soon after you found the religion, and you can only build cathedrals in half your cities. Holy city building gives health to all cities on its continent, and doesn't reward spreading Cao Dai.
Christianity
Era: Medieval (shouldn't this be Classical?)
Basic religious buildings are standard, but there's an extra one: the citadel, which gives big defensive bonuses, xp to siege weapons and an extra trade route. There's also an extra building you can make once you reach the renaissance, which doesn't require Christianity to be the state religion and gives several minor bonuses. Holy city building gives gold. Three world wonders: the King's Crusade spawns crusaders and speeds up great generals, St Mark's Basilica gives a permanent bonus to all water plots, and the Holy See Library gives science and espionage.
Confucianism
Era: Classical
Basic stuff is mostly standard, but give a minor bonus to science and gold. Holy city building gives a bonus to troops. Two wonders, both focussed on science.
Druidic Traditions
Era: Prehistoric
Together with Shamanism, the earliest religion you can found. Rather than the usual temple/monastery/cathedral configuration, you get three tiers of building. Only half your cities can have the tier 2 one, and only a quarter can have the tier 3 one; but on the bright side you can build everything straight away and the later ones give free promotions. You can build addons giving you +2% food for each vegetarian bonus resource in the city's vicinity. Shamanism and Druidic Traditions are founded off the same technology, so if you found one you can probably found the other if you want.
Hellenism
Era: Classical
Monastery gives more science than usual. Cathedral gives less happiness, but this is more than compensated for by the Odeon, an extra building giving happiness and education. Monastery also gives out a promotion to units built in the city, giving a decreased upgrade cost and a bit of strength. Holy city building gives science, and gives enemies war weariness. Has four wonders, giving a mix of bonuses.
Hinduism
Era: Ancient
Standard religious buildings. Extra buildings giving tiny amounts of culture for cows and elephants, and a small science building if you have caste system. Can build three national beliefs that help with crime, like Buddhism. Has some wonders and buildings which are shared with Buddhism. Holy city building gives gold. Has two separate wonders which reduce whipping anger by 50% each as well as giving other bonuses, and a third giving happiness throughout your empire.
Islam
Era: Medieval
Gives more happiness than usual for being a state religion. Holy city building gives gold. Has an extra building giving 1 science. 4 world wonders, mostly giving trade.
Jainism
Era: Classical
Basic religious buildings give extra gold, but reduce military production. Holy city building gives gold.
Judaism
Era: Ancient
Basic religious buildings give health bonuses. Holy city building gives a lot of gold. Three wonders: Solomon's Temple gives science, the Masada buffs priests, and the Ark of the Covenant both buffs priests and gives a ton of happiness.
Kemetism
Era: Ancient
Basic temple gives an extra gold. Has two extra buildings to make culture, and holy city building makes culture and gives all specialists in all cities an extra culture. Two world wonders, giving schools of scribes in every city and bonus science, respectively. Also has three national wonders, which give culture in all cities and various other benefits.
Mesopotamianism
Era: Ancient
Instead of the usual temple/monastery/cathedral, this has 5 religious buildings. Each gives a promotion to various classes of pre-gunpowder units. There are also expansions giving bonus food from carbohydrates in the city vicinity. Holy city building gives gold and culture. Has 3 wonders, giving free courthouses, contact with civs on the same continent, and military bonuses.
Mormon
Era: Industrial
Lacks a cathedral, but gets a similar building which can be built alongside the temple. The monastery equivalent is a national wonder, but doesn't go obsolete so you can keep sending out missionaries. Holy city building gives a big bonus to gold and science based on how many cities have the religion.
Naghualism
Era: Classical
Basic religious buildings give gold, culture and espionage. If you manage to snag an Native American culture, the religion also unlocks the Ball Court which gives happiness, gold, culture and xp. Holy city building gives gold and culture, and free specialists for each mining/quarrying resource in the vicinity. Has four world wonders, mostly based around sacrificing people.
Ngaiism
Era: Ancient
Has an odd arrangement of buildings. The base temple allows you to make missionaries and gives the usual temple benefits. Two other buildings give combat promotions, and the final one gives almost nothing by itself but can be further upgraded to give big food and hammer bonuses from cows, sheep and pigs in the vicinity. Holy city building only gives culture.
Rodnovera
Era: Classical
Temple gives an extra gold. Otherwise pretty bare bones. Holy city building gives gold.
Scientology
Era: Atomic
Virtually no culture, happiness or science, but generates lots of gold instead. The holy city building, surprisingly enough, gives you lots more gold.
Shamanism
Era: Prehistoric
Very much a parallel of Druidic Traditions; pretty much the only difference is that the addons give you +5% food for each meat-based bonus resource instead of vegetarian ones. Shamanism and Druidic Traditions are founded off the same technology, so if you found one you can probably found the other if you want.
Shinto
Era: Ancient
Exchanges most of the usual happiness and science buildings for maintenance reduction and military bonuses. Holy city building gives gold and culture. Two world wonders, improving water plots and pillaging respectively.
Sikhism
Era: Renaissance
No monastery. (Missionaries can still be built, though.) Temple and cathedral give +1xp to archers, melee and gunpowder units. Holy city building gives gold. The basic benefits of the religion are also relatively good, giving small bonuses to gold, science and culture.
Taoism
Era: Classical
Fairly generic temple/cathedral/monastery, although the monastery gives a the martial arts promotion to melee and recon units. Holy city building gives gold. Three world wonders, all of which give benefits in all cities.
Tengriism
Era: Prehistoric
Doesn't have a monastery or cathedral. The basic temple building gives +15% military production, and there are several upgrades you can build which give combat bonuses to mounted units. You can also build horse trainers in all your cities provided you have a single horse. Holy city building gives gold and culture.
Voodoo
Era: Medieval
Can only be spread by missionaries. The basic temple is weaker than usual, giving up most of its usual benefits for a minor decrease in unhappiness from sacrificing population. The cathedral gives extra production and gold, and the monastery gives production and commerce instead of its usual science bonus. The holy city building gives gold, and the single wonder allows you to make the rather powerful Hellsmouth dog units. The monastery also allows you to make an improved worker.
Yoruba
Era: Ancient
This religion has five buildings: a basic temple, and four upgrades. Uniquely the upgrades can be built in any city with Yoruba in it, not just the one where you built the original temple. The base temple is nothing to speak of, but the upgrades give a significant food, hammer and commerce bonus from seafood and deer, a great people birth rate increase, a reduction in maintenance and a small bonus to military production. Holy city building gives gold.
Zoroastrianism
Era: Ancient
Zoroastrianism offers above average happiness if you choose it as your state religion, especially in cities with a sky burial tradition. The holy city building gives gold, and also gives culture in all cities. There are four wonders, all giving benefits that will help a larger empire. Zoroastrianism dislikes slavery, so you'll get a bunch of unhappiness if you have zoroastrians in your empire and are running that worldview.
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