Grand Theft Auto III - and then some.
At first glance, Vice City will appear to be the same game as GTA III, but as you become immersed in the game you will realize that it is far more. More vehicles, more interesting characters and more missions with more possibilities to spend the money you earn.
Not to mention that the entire game takes place in the 80s, which leads to an award-winning soundtrack including all the greatest hits of the decade. Everything including the clothing style and cars fit the time period perfectly.
With more areas than GTA III, there is even more to discover including but not limited to new secrets and more storing space for vehicles you may want to keep.
Grand Theft Auto: Vice City has made me a firm believer that the perfect sequel is the same game, but with slightly more features and set in the 1980s.