Despite the huge necro, here are my two cents.
5 - Ceremonial Burial: +1 Happiness for each City following Religion
Unbeatable when going wide. This is one of the easiest sources of happiness you can get, if you can manage to pick it up.
5 - Church Property: +2 Gold for each City following Religion
If Ceremonial Burial isn't available, this is the belief to go with for wide. The bonus is incredibly powerful to your early-game economy.
3 - Initiation Rites: +100 Gold when each City first converts to this Religion.
Powerful in the early game, but it's hard to do anything meaningful with this unless you go full ICS, and even then, the mid-late power granted by Church Property is too powerful to make this belief worthwhile.
4 - Interfaith Dialogue: Gain Science when a Missionary spreads this religion to cities of other religions
Powerful, but it takes effort and a high Faith production to have any worth. I dislike it personally, because it requires letting other religions become powerful in cities before you spread to them, and penalizes early power, because, again, you have to let other religions grow first. I understand that some people experience great success with this belief, however.
2 - Papal Primacy: +15 to Influence resting point with City-States following this religion
A very mediocre belief. If it were +20, it would be great for maintaining friendship with city-states with a pledge, while not requiring investment into the Patronage tree. However, +15 is utterly useless, as the only thing it does is make friendships permanent with Aesthetics. Needs buffing.
3 - Peace Loving: +1 Happiness for every 5 followers of this religion in non-enemy foreign cities.
A poor belief. If you're in a situation where you need the happiness, you're going to have enemies. It does have better utility in the upper difficulties, where AI cities are liable to become enourmous and have mixed religions, but it's inferior to Ceremonial Burial in that you both don't get bonuses for spreading to your own cities, and need at least 5 followers in all cities following it in other nations.
0 - Pilgrimage: +1 Faith for each foreign city following this religion.
Since buffed to +2, this is still a piss-poor belief. If it were buffed to, say, +5, or dare I say, +10, this would become a viable belief. But as it stands, this is an utterly rancid belief. +2 faith? I'll take CP, and get +2 gold in my cities, too. Or +1 happiness from CB. A poor reward for a difficult target make this belief the weakest.
4 - Tithe: +1 Gold for every 4 followers of this religion
Playing tall? Then this is the equivalent of Church Property for you. I don't quite understand why people seem to like this one so much: You need 8 followers in a city to even hit the same number as CP, and 12 to surpass it. All in all a pretty amazing belief, but CP and CB outmatch it for anything but tall.
5 (if playing culture with strong faith and first or second religion) 2 (otherwise) - World Church: +1 Culture for every 5 followers of this religion in other civilizations
This is an incredible belief for playing culture, allowing you to easily gain over 100 CPT from it. In my last game playing with it (Byzantium, beliefs were DF, WC, Cathedrals, Itinerant Preachers, Feed the World, and Religious Texts), I was gaining 136 CPT in the Renaissance. This was a Huge map, but the power of it is obvious. If not playing for culture and to specifically exploit this belief, however, this is a garbage belief, providing marginal culture instead of gold or happiness.
