I'm not a huge racing game fan but I have found GT5 to be very addictive. Especially with the online racing community. You never get bored because there are always new people to meet and race with. Plus, it is simple enough even a gal like me can figure out!
Its a very Loaded Question.
It all depends on if you Just want Arcade type FUN, or Serious Racing / Simulation.
Best Simulation / Best 1080 Graphics, goes to GT5
Theses are all 720 graphics and very Arcade based racing.
FUN yes, but not as REAL as GT5.
Sonic and Sega All Stars Racing Transformed is probably my favourite PS3 racing game as far as arcade racers go, however Wipeout HD (and its Fury expansion) is also very good in that regard. Wipeout HD in particular is incredibly challenging, so that's fun.
For more realisitc racing games, I enjoy Gran Turismo 5, and Dirt 2. I didn't really enjoy Dirt 3 very much as the gymchana stuff tends to get on my nerves. I'm always compelled to get the Platinum medals, but gymkhana makes it very boring to do so. I like driving a good line, and the thrill of racing, neither of those aspects feature in gymkhana.
Gran Turismo 5 can be kind of tricky to get into I suppose. I assume you meant to say GT5 in the OP rather than GT3, Gran Turismo 5 is a pretty solid game but the campaign (A Spec) is pretty boring. Although I enjoyed unlocking new cars and experiencing the diverse, and accurate handling models of all of the vehicles. The best experiences to be had on GT are probably through online play, but the online setup isn't so great unless you get involved in racing communities. Jumping into random races online is often poorly balanced (in regards to the cars you're able to use / competing against) and the drivers often have pretty poor racing ettiquette.
As much as GT5 is a good game, you're probably not going to enjoy it all that much unless you're a hardcore simulation-based racing fan.
I recocomend Gran Turismo 5 if you're into realistic drivers, Dirt 3 if you enjoy some real driving mechanics but not insane and Motorstorm if you just plainly enjoy racing games for the heck of it.