I'm not going to get into this discussion but from my experience the Xbox was a lot more powerful on paper but the Gamecube came pretty close in real world performance. Some stuff I distinctively remember from last gen:
- Sony and Microsoft published spec sheets with the absolute maximum performance peaks of their systems. When Nintendo gave us some real world performance stats people were shocked and thought the Gamecube was much weaker than the PS2 even
- The PS2 was the weakest system by a good margin but most games were heavily optimized for it due to its large install base
- 3rd party games looked worse on Gamecube because developers didn't put any effort into them. Need for Speed Underground 2 on Gamecube looked worse than its predecessor... this was often the case. The Gamecube had by far the lowest install base in the west (and smaller storage... and "3rd party games don't sell on Nintendo systems") so western developers wouldn't put a lot of resources into the games. In real world performance the Xbox and Gamecube were pretty close but Xbox games had more resources put into them.