Definitely Burnout 2, for me. It took everything that was good from the first and made it soooo much better. It really just feels like the essence of Burnout, to me.
I really love Burnout Paradise from what I've played so far and it feels like a Burnout game from how the cars handles and such, but as you said it is a bit different. You have a whole map to just freely drive around and the racing takes place on it, rather than having separate more linear areas to jump into and race. You also had a countdown timer in Burnout 2, where you had to hit checkpoints in time to extend it, so it felt like a arcade experience a lot more.
I think overall I prefer Burnout 2, but they're both fantastic in their own ways. I need to play more of Paradise though to say for sure.
Burnout 2 also has one of the most fun multiplayer modes ever. The Crash mode where you have to crash into traffic and try and get the highest amount of damage score. So good!
( Edited 22.08.2016 10:57 by Marzy )