The XBox was more powerful, but the GameCube was a far more efficent design.
The XBox was a $400 worth of PC parts thrown together than MS sold at a big loss.
The GameCube was a $200 mini-monster. If Nintendo had given Art-X another $100 of budget to work with, it would've smoked the XBox.
Rogue Squadron II/III and Resident Evil 4 I still think are the two most impressive visual games from that generation.
Probably a good reason why MS dumped the XBox vendors and opted to choose IBM/AMD for the 360.