There hasn't been any recent releases, so there's nothing that can graphically compare to GTIII, though some games do tend to look sharper with high rez and FSAA and anisotrophic filtering.
Best game for the average player: need for speed: porsche Unleashed
Best game for the race enthusiast: nascar 2001 (is 02 out? maybe?)
Best game for rally: Collin McRae
Best game online: Need for Speed, Motor City
Start with Porsche Unleashed though, it's a pretty good racer and can be had for about $15 individually, or $20 in a four pack with a bike game, need for speed 4, and I think a monster trucker.