The games that I thought were really good on PS2 are Devil May Cry 1 not 2, Metal Gear Solid: Son of Liberty (came to X-Box), The GTA series (came to X-Box), Grand Turismo III(not a racing fan, but I have to give it props.), and I think that's about it besides the DBZ games, but they aren't to good I'm just a DBZ fan. I would have mentioned Final Fantasy, but I've never played them, not a turn based fan.
The games that I thought were really good for X-Box are Halo (My number one most played game and nothing beats system link Halo)Morrowind, Steel Battalion, any EA Game (specifically Fever and Top-Spin) Splinter Cell (came to PS2, but is better on X-Box), Star Wars Knights of the Old Republic, Soul Calibur II( I love Spawn), Rainbow6 3, Ghost Recon (way better on the X-Box, you can't argue with that.), The GTA series ( looks slightly better and you can customize the radio), Unreal Championship ( Fun with friends and Live) Mid-Night Club 1 and 2 (Again, not a racing fan, but system link CTF is really fun). I don't dis-like any system, a game's a game, but most of the games that I mentioned for X-box couldn't be done on any other system, Halo included. PS2 tried Splinter Cell, but it couldn't do what the X-Box did.