Here's my feedback playing on same settings as I've been using for previous patches (Prince difficulty, Huge map, Epic Speed) : the gameplay feels very different.
First up, I get 5 free happiness per city now, rather than in total? I think that's way too much - it seems that it's impossible for citizens in a city to be unhappy until it grows beyond size 6? Instead of happiness being the main factor limiting my expansion and encouraging development it's been a complete non-issue.
I discovered a couple of natural wonders within the first 100 or so turns, and have access to +1 happy per city via Progress, but I really haven't needed it. For what it's worth I think those are both excellent and feel much more useful than they did before, so that's great. The difficulty handicap on top of that though is making happiness feel meaningless.
You might guess that things were going pretty smoothly for me early-game as a result of this. Actually the game was rushing past a lot faster than normal. I founded a religion second (better than usual) and settled some very nice city locations, all while maintaining a reasonably strong military (about 2 units per city, including some horsemen).
At which point I noticed that the AI were doing even better than me. I knew Spain was doing fairly well because they founded around turn 100 (which is early but not unheard of). I didn't notice quite how well until they declared war on be and attacked with an army I've never seen the likes of this early in the games. I'm a very defensive player, and happily I had taken Goddess of Protection and was playing Shoshone who get a combat bonus in their own territory. So I was OK.
Looking at the map and the leaderboards though, I decided to call it a day. I might be do fine defensively, but all the AI on my continent seemed to be performing maybe 20-30% better than what I'm used to competing with. If I played this map again and knew what was coming, I'm sure I could manage. I have a feeling settler spam would be a winning strategy. That's not really how I like to play though.
To conclude, I should make it clear I'm not trying to shoot down the happiness overhaul. I think it's a great change, it looks like it will be a lot of fun, and it just needs tweaking in some areas. The handicap bonus would be my first suggestion.