I just saw
Carlito's Way this afternoon and it really is a lot like Vice City in some places. Of course, Carlito's Way is the tale of a criminal who wants to retire, whereas Vice City is about a criminal who wants to get higher up. But the characters and situations are really very similar, and I wouldn't be surprised if Carlito's Way was one of the movies the designers used as a reference.
Take for instance the lawyer from Carlito's Way and the lawyer from Vice City:
I thought it made the movie extra fun, you know, seeing the references.