I prefer its graphics to those of CIV4 -- they "pop" more. When I play games of Civilization IV, I'm always forgetting about units -- losing them. CIV also seems more complicated than Civ3, and I'm not comfortable with it because I don't understand its mechanics like I do CIv3's. Then again, I suppose if I made myself play it more, I'd learn the mechanics...but I've got the rest of my life to get around to that, I suppose.
I can't speak for Civ5, not having tried it. I'm very much interested in it now with Gods and Kings, but it's too expensive for me to try without knowing how I'll like it.
Has no one ever created a Civ3 clone on the Civ4 engine?