Vice city improved on what Grand Theft Auto Three was missing or had too much or not enough. Game was basically the same but the it is set in the 1980's and in Miami.
To me the only real differences were the actors who portrayed the voices of the characters (Ray Liotta, Dennis Hopper etc.) and some other small details such as being able to shoot out tires or ride motocycles. Even though Vice City had some big improvements I feel that doesn't have as much replay value as GTA3. Even though they are the same game pretty much. If you liked GTA 3 then you will like Vice City.