Alright, here are my feelings after about 10 hours logged:
1. Graphical style has already converted me. Wonders look much more like actual wonders, animations are much better, and tile improvements are more lush in regards to colors and actual activity. Also, having the leaders presented in the slightly more cartoonish way actually works quite well as they can pull a bigger range of emotions off with them and it doesn't look silly, as sometimes the leaders looked in V.
2. Changes to the policy tree are very nice and actually add some depth besides filling a tree out and then moving onto another one. Tied to that, the government changes along with the cards for policies make things much more personalized compared to V.
3. AI seems a little better gameplay-wise than V, but they are all *******s. Given, the game has only been out for a few days so maybe there are methods to working with them that haven't been sorted out yet, but the AI is just perpetually pissed off at you from my experience.
4. Changes to city states are awesome! Now you get envoys which you allocate to them rather than just spending gold to buy them outright, and as you allocate more envoys your benefit increases. This seems like more of a "realistic" approach rather than V where you just dumped money to buy them out, which always seemed rather off. City state is an ally of your enemy for 2000+ years? No biggie, just send them a couple thousand gold and they will flip to your side on the spot!
That said, there definitely is some stuff that needs worked out and I'm sure will be with time. You can sell military units on/off your tiles which is stupid during war (Unit at 10 health and about to die? Sell it for gold, even if you're half the world away!), camera doesn't snap back to units all the time so sometimes you'll accidentally misclick a unit and notice 5 turns later that they are making a 30-40 turn trip to who knows where, notifications are smaller and some are missing from side bar like your city being able to attack a unit, chopping trees has no limit and is OP as hell right now, and the tech tree needs some work as well. Eurekas are too good and they happen even if you're not trying to get them, and with the tech tree being thinner than V right now your tech outpaces your production fairly early in the game. Example of tech tree is the first game I played I hit the Industrial Era in 1100 AD without even trying hard to get there, whereas V you tend to hit it around 1400-1500 if you're going somewhat hard at it. Given I started the first game at King while I usually play on Emperor on Civ V, but this seems to be a common complaint throughout the community right now (along with Eurekas needing a nerf) so it's not just me!
All in all? Good times and definitely worth the purchase to me as a Civ addict, but for people who just play casually they may not notice enough of a difference between V and VI to justify dropping $60 right now.