I'm loving the game so far, but you should know this is sort of a "Civ light" implementation. A lot of the micromanagement has been pulled from the DS version, leaving you to focus largely on producing units and buildings, researching tech, and combat. You won't spend as much time fine tuning city needs and resources, and land improvements are automated. Roads between cities are bought all at once instead of built one square at a time by workers, for example. It seems designed to make the game easier to pick up and play and to shorten the length of a game--I played a couple of random maps through to winning, and both games ran between 2-3 hours.
The graphics are a little crude, which is surprising considering how nice some other recent DS titles look and how well-designed the full version of Civ now looks. (As of July 10th, 2008, Amazon is showing the PC/console version of the game in the screencaps above, so don't be fooled.) I don't mind the cartoon look of the characters, but the pixellated edges and dull blue top screen image between turns looks less than stellar. That would never make me NOT play this game, though, ha ha.
In general, the DS version feels like it's something between Age of Empires for the DS and the console/PC version of Civ.