That's a lot of crap. That has nothing to do with the fat model, it's just that if the lens of your PS2 is worn out, it'll be hard for it to read games and apparently this affects more some new games.
And yes the game is great on the PS2, just stay away from the PS3 version, because you'll have a hard time playing on the PS2 after playing on the PS3. Believe me I have the PS3 version but most of the time I play with my friends I play the PS2 version and my eyes literally bleed. It's not that the PS2 version has bad graphics, it's just that the PS3 version is gorgeous.