They're actually two very different cars. They were also my two first cars and the game, and I didn't part with either of them until I got gifted billions and could afford to try out somewhat better cars. They both lack aesthetic mods. You can change the exhaust on the newer car and you can give it a two-tone paintjob. That's about it.
The newer car is extremely stable. It has a wide turning radius and will actually understeer. It's handling isn't sharp (it's almost slow...), but it will hold it's course (almost stubbornly) and it can take a beating. Handbrake-induced powerslides lead to progressive oversteer that is extremely easy to control.
The older car isn't near as stable. It's actually quite loose by comparison. Turn-in is substantially quick (a lot quicker than you'd expect).The rear-end comes around with little provocation. Oversteer is sudden and handbrake-induced powerslides are spooky and very hard to reign in.
Personally, I prefer the newer version.