Take all the good from GTAIII and then add to it. That's basically what Vice city does.
You have the same gameplay from GTAIII, but the aiming for weapons has been imrpoved, and there are a few various extra types of vehicles you can drive.
The graphics have been imrpoved upon a bit, but the same pop up issues and blocky character models are in this game. Still, Vice City is around twice the size of Liberty City, and there is even less loading during gameplay (the city is split into 2 sections instead of 3).
More voice acting has been added, with real television and movie actors taking the helm of all the main characters; including porn star extrodinare Jenna Jameson (who plays, duh, a porn star in the game). Ray Liota also now takes the helm of the character you play; while in GTAIII your character was completely silent.
The addition of your character speaking actually adds to the game immensly, as it makes the story much more cohesive and helps it flow nicely.
The radio stations now have real music from the 80's, including songs from Michael Jackson (2 songs), The Buggles, Toto, Iron Maiden, and a lot of others. My only gripe is the talk radio station isn't quite as funny as it is in GTAIII, but it's a small thing. Also, Couzin Ed is in the game as a caller to VRock; most of you won't know who he is but he is a DJ on a radio station in the Philadelphia area, which I think is a cool touch.
All in all, this game is a great sequel to a great game. IF you don't own this game, go out and buy it...now.