I like GTA3 because it was the first GTA game I'd ever played, and it didn't just focus around a single element like Vice City did. It had you working for a Mafioso-esque organization, an Asian crime syndicate, a Hispanic street gang, and a few more characters that were unique in their own way.
Vice City's missions, on the other hand, didn't seem as lively and varied as GTA3's. Don't get me wrong, Vice City is a great game, one of the best. But in my humble opinion, GTA3 is the best. No doubt about it.
That's actually a very good point. GTA3 lacked the side missions and mini-games Vice City had. GTA3 had missions and the packages - and that was about it. Vice City had mini-games, sidemissions, property to purchase, more vehicles and whatnot, etc., etc.