I haven't played Rivals but I love the Need for Speed Hot Pursuit games and the PS3 version is no exception. Fantastic game. If you like cart racing I recommend Sonic and Sega All Star Racing and another fun one is Split Second
split/second is probably the best arcade racer I played that gen (or since).
There are various event types, but the main mode is kind of like cart racing, with big track-deforming explosions.
Cars themselves don't shoot, it's all done by unlocking remotely-triggered trackside explosions.
Very satisfying. I've never played anything quite like it, and very much wish they'd make another one.
Fairly early on, one spectacular special event is unlocked--Racing laps on a circuit filled with trucks dropping exploding barrels. Score+time bonus is earned for each truck passed. Once I unlocked it I didn't make much more progress in the game, because it turned into lengthy sessions of me playing that one stage for high score. I repeated the same trend when I bought the psp and pc versions of the game.
My opinion is the 360/PS3 era is when racing games went to shit. I can't say I like any of the big racing titles on the PS3. The Need for Speed Hot Pursuit game on the PS3 was one of the least enjoyable demos I've ever played. The demo for Burnout Paradise literally made me barf, so I can't say I liked that one.
The only racing game I've kind of liked on the PS3 was Sonic All Stars Transformed Racing.
But generally speaking, when I want to play a racing game, I play Need for Speed Hot Pursuit II on the PS2 or something older.
The demo left me with doubts but Blur turned out to be a really good arcade racing game. It's fundamentally similar to Super Mario Kart, but cranks down the cute to 1 and turns up the impact and mind-blowing special effects to 10. You can also directly attack opponents, a feature that would have made Split/Second a lot more enjoyable.