I haven't finished my comparison & re-evaluation game yet, but I'm going to lay out my conclusions anyway.
Civs 5 and 6 both have some annoying design flaws or outright bugs (like most games). 6 has a lot more of those than 5 does. I'm sure we've complained about them extensively in this very thread already. By way of example, consider the apostle bug. New apostles start at level 2 and receive a second promotion until you reach the Atomic age. Then those promotions suddenly stop. Yet you still get the "unit has a promotion" flag on the right side of the screen. So...do the promotions stop according to some undocumented design, and the flag is just a feedback bug? or are promotions themselves simply broken? Whichever it is, this bug has been around since the first version, and it makes a religious victory much, much harder if you haven't already gone well down that path before the promotions dry up.
6's deeper strategy makes 5 feel like a beer-and-pretzels wargame. The warmonger penalty makes war much more costly as the game goes on, so 6 is much more about building than about conquest. That can make the late game boring. 6 has a better diplomatic model, IMO, with better info about why the AIs like or dislike you. However, trade deals nearly always favor the AI.
City states are weaker than in 5. I miss the UN votes and victory path.
Aside from the bug, I like 6's religious combat model; it gives you something to do when you can't wage conventional war. At the same time, that can get annoying when the AI takes advantage of it -- you have to be constantly vigilant, and for some sadistic reason religious units don't have the Sentry ability so the AI can easily sneak missionaries and apostles past you.
I did like the way 5's happiness model eliminated the early land-grab and slowed down expansion. In 6, the map is going to fill up to capacity fairly quickly, whereas 5 could often go into the endgame with lots of open terrain left. The sheer number of cities in 6 can get overwhelming...especially since they removed the build queue for some sadistic reason. Theoretically, I prefer 6's city-by-city happiness model to 5's global happiness, but I don't like that consequence. Maps in 6 feel more crowded even before they get covered in city spam.
I'll just cut to the chase rather than rehash any more complaints that this thread already covers: I actually prefer 6 despite its many flaws, and I'm not going to revert to playing 5. That is not the conclusion I expected to reach. But I'm more of a builder than a warmonger, and 6 suits my style of play. I just wish they fix and improve it. The game model is better, but the execution is not.
Hope that helps you reach a decision, Carpet. There are things to like and things to dislike about 6, and yours won't match mine...but there it is.