Burnout Paradise does suffer from some Rubber Band AI issues, but mostly it plays fair in the Race events. It's possible to get into the lead and stay there if you pick a fast car, drive reasonably fast in the straightaways, and corner carefully.
During Marked Man events, however, it does not matter how fast your car is or how many of the other cars you take down. Cars will catch up with you even though you should have a commanding lead. The game even spawns cars going beyond top speed to catch you in if you take them all down. I've run these with what should be the fastest car in the game and still not been able to outrun them.
Road Rage events seem to be kind of backwards - cars seem to slow up to let you catch up and take them down most of the time. New cars that spawn (or, I suppose respawn) might overtake you, but then they kind of coast a bit so you can catch up. It's not unusual in these events for me to get a takedown "Rampage" or similar.
Also worth noting - during a takedown animation, your car gets to play by the "cheating" physics rules and won't crash in some situations where a crash seemed inevitable from your perspective.
The other events don't really have opponents (except the clock) so there's not a lot of AI cheating to be had.