Nintendo is all about platform games. Since Mario, Luigi, Banjo-Kazooie, and Donkey Kong specialize in platform adventures, GameCube owners have plenty of this ever-popular genre.
Sony does not specialize in platform games. But with the PlayStation2 library at 400 games, PS2 owners have plenty of platform games to choose from.
Xbox, on the other hand, is a little platform-challenged. There was an awful awful game called "Azurik: Rise of Perathia" for Xbox. I think a Crash Bandicoot game came out for Xbox, and "Max Payne" was sort of a platform game.