There are plenty of good games on GameCube. Most of what you like on Xbox is likely to be available on GameCube as well.
If you like RPGs, you might like Final Fantasy Crystal Chronicles, Skies of Arcadia: Legends, Tales of Symphonia, Phantasy Star Online or Lost Kingdoms, which are all available exclusively on GameCube. (although Skies of Arcadia is a remake)
As a GameCube owner, I must also recommend Mario Sunshine, Zelda: Wind Waker (my favorite game ever), Super Smash Bros Melee, Animal Crossing, Rogue Leader, Pikmin, Sonic, and Super Monkey Ball.
Given that you are only 12 years old, I don't know if your parents let you play violent games, but if they do, I would strongly recommend Eternal Darkness, Resident Evil (any), Splinter Cell, Metroid Prime, and Metal Gear Solid: The Twin Snakes (upcoming).