Here's my take on the topic. But first, some biases:
1.- I've only really played Paradise, which is absolutely amazing.
2.- I've always wanted to have Burnouts 3 and 4 because I played the XBOX demos for them. Sadly, my PS2 emulator needs something bigger than an i5 with an nVidia GT540 to run smoothly somehow.
3.- I've spent about 2 rt days of my life in the burnopedia.
Here's what I think: Paradise comes here trying to reinvent burnout back to what it was in 3 but with the posibilities an open world can offer. IMO, they only lack 1 thing, and it's the checkpoints they implemented in Most Wanted - After a couple of hours, all the races become just a search of a prefixed, straightforward route to the finishline you know from previous races. 4 was AWESOME, but traffic checking was indeed too happy - I don't care it's from behind, if I'm doing 185 and crash against a semi, my car becomes wrecked INSTANTLY, unless the semi is going at the highly implausible speed of 184. I did, however, like the fact that you could use the Crashbreaker after a big crash, because it gave more opportunities of aftertouch takedowns, which are much needed when using a lower tier car. 4 also has the upper hand on 3 for graphics, but that's about it.
You realise after not much time that paradise is basically a memorial for the entire series: Kitano Hydros Techno, for example, sports the license plate "B2-JP-CC" (Burnout 2 - Japan - Custom Coupe) and it's basically the same car. White Mountain and I88 are mentioned, as well as Big Surf. The Watson W16-25 Revenge is the Revenge Sports or something like that from Revenge. It comes with 3 nitrous styles, Speed (which is BO1-2 boost), Attack (Which is BO3-R boost) and stunt (which is a simple nitrous). The cop cars have the cop code that cop cars in 2 have. It does a pretty good job at representing the rest of the games, but it fails in the circuits. I still have a lot of fun with it though.
Burnout 3 seems like a pretty "basic" game meant to have absurd amounts of fun: Fast paced racing on cars that can destroy each other with a huge nitrous tank and pretty good circuits and intersections to crash. Crash mode was indeed better in Revenge (MUCH better, I'll add), but it's not a big deal. The story mode seems to be the larger of them all (I played a bit at a friend's and couldn't get more than 2% done) and the car amount is pretty reasonable.
But as I said, I've only really played Paradise, and it actually only has 1 downside. My vote, upon further investigation, remains null.