I haven't played the PS1 games, but my selections are...
GTA3: Taxi. I loved the control on them, especially their ability to easily back up and do a 180 real fast. They were so versatile and resilient, just perfect for the variety of jobs n the game. The only time they were a problem was when I needed serious speed, at those times I would use a Stinger.
Vice City: COMET! I have pulled some CRAZY stuff in Comets, their controls are amazing. They blow up pretty easily though, so sometimes I'll use the slightly tougher (and far mroe common) Cheetah. Cheetahs are also better at high speed 90 degree turns if you know how to use the hand brake right. Of course sometimes you need to use a bike, with the PCJ being the obvious choice there.