I actually think there is something in both you could like. The reasons why I asked those questions are as follows:
1. CiV is tailored towards smaller, more specialized empires, although big ones are certainly possible. CiV also allows for those, but technically there is no trade-off to having a gigantic empire on the long run, whereas in CiV every new city ups your cultural costs (more on that in a bit). That's apparent even in the way National Wonders work. These are buildings that every civ can build only once, however they have certain requirements. In CIV to build the Oxford University for instance you need 8 universities in your empire. In CiV you need one in
every city you have. Which also makes One-City-Challenges a lot easier.
2. In CiV you can have a relatively small, tight army that you consistently upgrade over the ages. It's very rare that a civ has more than 20 units at once until the late game, while in CIV that would just be a moderately sized stack. Luck has also been taken out of the equation - just like in III, in IV whenever one unit attacks another, someone dies, and even though there are calculated odds every now and then we all know what happens.
. That's gone in V. Every unit has 100hp and it takes around 3-4 attacks to kill. Luck has essentially been taken out of the equation. This
doesn't happen. Ever.
The flipside of 1UPT though is, well, in later stages when you have dozens of units it all might turn into a bit of a clusterf*ck, pardon my French.
3. CIV has
civics. They essentially govern different aspects of your empire (religion, government and so on). 25 in total, 5 in 5 categories, 23 of them bring only benefits, and 2 have some sort of a trade-off. Each requires a certain upkeep to be paid, but that doesn't really matter unless you are playing on Emperor or above. Techs unlock them, they can be switched when you feel like it which causes Anarchy, just like old times.
In V there are no civics. Instead you get
Social Policies, although the name is misleading, they are more like the traditions and culture of your empire. There are 50 in total and they all bring benefits only. As you can see, there are different branches that lead to different parts of each tree, which brings some strategy into the mix. And do note, it is absolutely impossible to get all of them. They are acquired by generating culture, which comes from buildings just like III. However the cost of each increases gradually, every additional city increases the cost further, meaning that the bigger your empire - the fewer SPs you will get. They are also tied up with the Cultural Victory - while in IV all you have to do is raise you culture to 50 000 (standard speed) in 3 of your cities, here you have to finish off 5 of the trees, which unlocks the Utopia project. In IV bordering territories could flip in favour of the city that generates more culture. Even a whole city could change sides, a peaceful conquest, which unfortunately also meant that conquering a city in the late game was a really bad idea, as it would quickly flip back to its owner or another neighbour. Nothing of the sort in V.
4. In CIV you unlock religion by researching a tech. Your holy city gets picked at random when you found one, and they are all interchangeable, it doesn't matter if you are a Buddhist or a Christian. Adopting one gives gives you +1
in cities that have adopted it, and you can build 3 religious buildings - Temples that boost your happiness and culture, Monasteries that give science and culture, and if you have enough temples, cathedras, those increase your culture output significantly. If you have found a religion, you can use a Great Prophet to build a special building in the holy city that gives you 1 gold for every city that follows the religion. Religion itself spreads automatically, or you can use missionaries. One missionary converts one city. You can found
all religions in the game, however only one can be your state religion.
Religion in CIV has a
gigantic influence on diplomacy until you adopt the Free Religion civic. Most, although not all civs, will love you or hate you based entirely on your religion and nothing else. On one hand it makes it easier to form diplomatic blocks early on, on the other, well, it's kind of stupid really. In my last CIV game I converted a neighbouring Caesar to my Confucianism and we were friends for thousands of years. Then he found Taoism, converted to it, and attacked me just because I was following a different religion. 2000 years of cooperation and trading down the drain.
In V religion is modular and you can found only one. To do that you need faith, which is generated by buildings, just like culture. When you have generated enough, you can found a Pantheon, a sort of a proto-religion, and can choose between 23 pantheon beliefs, which mostly are tied to different terrain types. Do you have a lot of stone near your capital? Get Stone Circles, it gives +2 faith from quarries. You want to turtle up? Get Goddess of Protection, which gives +30% range combat strength to cities. After generating even more faith, you get a Great Prophet and can found a religion. You get to pick a Founder belief (a bonus you get out of the religion, 13 in all) and a Follower Belief (a bonus that everyone that follows your religion gets, 16 I think?). With a second prophet you can buy an Enhancer belief, which speeds up the way your religion spreads (9 in total) You can create a religion that boosts your research or generates gold every time you convert a city. Some religions benefit from being spread, some don't at all. With the faith you generate you can buy missionaries to spread it further, inquisitors to exterminate a foreign religion, and different buildings and even military units, if you chose the necessary beliefs. Religion is spread in a linear fashion - each city "pressures" other cities within a radius of 10 tiles, converting one citizen at a time.
Religion has a very limited influence on Diplomacy. Following the same religion does give a boost, having a different one doesn't make a civ hate you unless you spread yours aggressively with missionaries or Great Prophets, who can also be used as a sort of a super-missionary.
5. In IV roads cost nothing, just like in III. In V they cost maintenance. Some love it, some hate it. In IV cities cost maintenance. in V some
buildings do.
6. Tech trading is gone, now you can get Research Agreements. They cost money and boost your research. The bonus is calculated as 50% of the median Science value for all of the technologies the you can currently research, which means that it's in fact a bad idea to have RAs with the tech leader, because he benefits more than you, so that brings some strategy into the mix. The only way to actually get a tech out of another civ is to steal it with a spy.
There are many other details that you might like or hate. Diplomacy for in CIV is centered more around religion and trading, while in V you can make promises, and if you break those, you get a diplo hit with all civs. Warring a lot also gets you a diplo hit. Generally the diplomacy in V was dreadful, but has been much improved in the expansion, I think I like it more than IV. City states have a singificant influence on the game - tiny one-city civs that give quests. If you complete those or if you give them money, you can become Friends and even Allies with them, and they give you some kind of a bonus, whether it's extra food, culture, faith, military units or happiness. They also go to war for you and have a vote in the UN, so they are essential to the diplo victory. You can pledge to protect them or bully them, but beware! If a civ bullies a city you promised to protect, or if you bully one, it might lead to some trouble.
Overall, seeing as you are mostly on the fence about many aspects, try out the demos of both games. I think you will like something about both, so just try them out. However, do NOT try the CiV vanilla demo, there is a Gods and Kings demo, get that. If you had asked me only a couple of months ago which one to get, I would have said IV without even thinking about it. After the expansion though... It's a much better game now.