PS2 had FFXI... But Gamecube had a lot more games that I cared about, like Super Smash Bros. Melee, Fire Emblem PoR, Skies of Arcadia Legends, Luigi's Mansion, Legend of Zelda Master Quest, Wind Waker, Twilight Princess, Eternal Darkness, and Metroid Prime...
Damn you for asking this question, Mrs. Niflheim! Respectfully!
I guess I go with the Gamecube though. It's more enduring, as mine still works, whereas my PS2 started to bug out around 2010 and can't even watch DVDs or Blu-Rays that have more than 13 chapters/sections for some reason, freezing up on any that do. And I moved over onto PC for FFXI in 2011, anyway.
Plus, you know, with PS2 I always had to hear about the whole, "You're holding the group back because you're on PS2 and don't have / can't have Windower!!!!!!!!!!!!!!!!!!11111"
So Gamecube.
Say your favorite new age pop singer
or
Say your favorite new age tech piece/software that didn't exist in the early 2000s.