I still think the GameCube honestly still had better 3rd party support. Most major 3rd party multiplats were day 1 on GCN and it did have some exclusive/premiere titles that were notable like Resident Evil REMake, Metal Gear Solid: Twin Snakes, Final Fantasy: Crystal Chronicles, Viewtiful Joe, Super Monkey Ball, Tales of Symphonia, Phantasy Star Online (for some weird reason), Resident Evil 4 was exclusive for a bit.
Obviously that didn't quite match up with PS2 having GTA3/VC/SA, Final Fantasy X/XII, Tekken, MGS2/MGS3 of course but still.
Things like Madden NFL, Prince of Persia, Beyond Good & Evil, the James Bond games, Soul Calibur 2 w/Link, NBA Street, SSX Tricky, Spider-Man, Tony Hawk, Splinter Cell, Call of Duty Finest Hour, The Lord of the Rings games (these were actually pretty good), Enter the Matrix, Need For Speed, Baldur's Gate, TimeSplitters 2, Sonic Adventure 2, Skies of Arcadia, etc.