Sirius,
The main complaint is the multiplayer. Its choppy as hell. There aren't even unit animations in it. For me, that isn't a big deal, as I mostly play single player games.
They took out a lot of things. It seems like it tries to mix Civ IV and Civ: Revolution (the console version). Everything is a lot more combat-oriented now. Stuff like the gold/tech sliders are gone, religion is gone, civics were replaced by permanent 'social policies', etc.
Once I got the game up and running (I have an older computer, so had to run the DX9 version) and settled into the new UI, I enjoyed myself. Honestly, the thing I miss the most is the in-game real world clock.
I'm sure there are a million things I could say, but they've all been said on the Civilization Reddit and the Civ forums. I would read some of the stuff there: http://www.reddit.com/r/civ/
I can answer any specific questions, though