Depends on how much you care about slightly better graphics, much improved save times, and quicker load times. Slightly quicker load times, smoother framerates and drastically improved save times are three of the most common upgrades games would get in the Xbox releases, though there's other games (like Fatal Frame II and Burnout 2) that'd receive additional content that would never see release back on PS2 or Gamecube (though some would get ported back to PS2 in subsequent rereleases, such as MGS2 and Silent Hill 2).
Save times on the Gamecube are extremely peppy on average, but on PS2 they can be agonizingly slow. Thank god some games (like Ratchet & Clank, Jak & Daxter, and Sly Cooper) find creative ways to hide the loading/saving times, because even on smaller saves it's a pain in the ass.
Framerates can be spotty in PS2 and Gamecube versions of multiplatform games (particularly because most of them used the PS2 version as the basis for the GC version), though a couple of games came away looking really good (Gamecube version of Beyond Good & Evil and I hear the Gamecube version of Warrior Within?). Still, the majority were smoother are the Xbox.
Yes, but for the life of me I can't remember any examples off hand. It's something I didn't pay too much attention to since I never could get my dick beaters on a set of Gamecube component cables.