I loved IV and have played tons of hours with it. When V came out, I tried it for a couple games, but grew bored and went back to IV, and have played only IV in the last five years. I just got VI and am really trying to make a go of it. There are some things I really like, but other things I don't like. I haven't played VI enough to give my ultimate opinion, but I'm trying to make the best of it. From the IV perspective:
Movement seems really slow, and it can be frustrating to have a movement point left, but because of the terrain you have to wait until next turn. To help somewhat, I'm using a mod that increases movement by one. This mod has been a big help, but it still can take an eternity to move great distances. Also, roads have been nerfed, and the roads that route Traders make don't increase speed much, so that is frustrating. Still I like the Traders idea, but they take to long to make a route. I wish this could be buffed a bit and have the ability to make more roads more easily.
1UPT. In concept I'm OK with it, but the AI can't handle it, and it is very frustrating when there are blocking units which can stop you. So, to me some stacking is required. In response, I've been using a mod to allow multiple units per tile, but the problem is that the AI doesn't know how to use it and I don't know if it can be programed to do so. Because of that unfairness, I've been limiting myself to 2UPT, though I'd really like to increase it to 3-4. I used to have huge stacks with IV, but we don't need to go back to that extreme.
War weariness and warmonger hating is too extreme. I'm also using a mod to even this out.
Production is way too slow, and can create some boredom waiting for things to build. This is one reason you will only have a fraction of the units you have with IV. I think this can be fixed though.
I really like the districts and different buildings for them. It's amazing to use different tiles around your city to create them.
Health is back after missing from V, in the form of housing. It is an interesting and different concept on it. However, the bonus resources for them don't have the same effect on buildings like IV had. They are basically all the same, but different names, so that is a little boring.
The amenities from luxury resources is interesting too. You really need to focus on getting as many as you can. I do a lot of trades with the AI for gold on this, because they don't like to trade them 1 for 1.
Builders are a totally different concept, and I kind of like it, but you need a lot of them. I think this should be buffed.
Graphics: I really like them, especially when zooming in. However, without the icons, it is very hard to tell what is what, unless really zoomed in, which is not how you would play IV. The unit size is much smaller than IV, which is bad for gameplay but looks really good.
Embarkation: Transports with IV gave a lot of strategy, I thought. However, I'm not disliking embarkation as much as I thought I would. One downside is that I hardly build any naval units.
There are a lot more different features that VI has, that I haven't talked about. I'm still very new to the game though.