This game is far more complex than Civ 4. Civ 4 is awesome because over the decades they game has become incredibly streamlined and the game has a general big budget polish. But it's also pretty straightforward, Civ 4 never got "boring" for me but the games frequently played out the same way, and they really bogged down once you got to the late game.
Dominions 3 on the other hand will take you hours and hours just to get a handle on the game's intricacies. Then after you think you've got a handle on it, if you play as a different nation it's like starting all over. And there's so many nations, even the vets haven't necessarily played them all. This is a good thing though, this game will keep you occupied for years if you want it to. The incredible complexity of Dominions 3 makes it the perfect game to get lost in.
Civ 4 wins on graphics and streamlined interface, but part of playing Dominions 3 single player is learning how to manage your nation with the minimum amount of micromanagement. Once you get it figured out the game moves at a good pace. I play full games with me vs. all the AI nations and turn generation is usually under 5 minutes on an old crappy laptop. For a reasonably powered desktop I think turns can generate in a minute or two. This is also subject to how you set up the games. If there are 1500 provinces of course the turns will take a little longer.
You can also read a review of it here:
http://www.odstudios.com/article.php?anum=311