PSX to N64 is a very different case. The PSX hardware wasn't really designed with 3D graphics in mind, while the N64 was built from the ground up to do 3D graphics. Everything about the PSX hardware was inferior in power to the N64. The reason the PSX won is because of it's optical media, and relatively easy programming. The N64 is still known as the Mt. Everest of coding, but some say the PS2 has it beat in that department....
Anyways, my point is that the Xbox touts higher specs than the GameCube, but the amount of power that can be actually used is FAR less than those specs would indicate. The GameCube exceeds it in power in some areas, and makes up for it's shortcomings in other areas through its incredible efficiency.
Most gamers will tell you the Xbox is better because it has higher numbers behind its name.
Most hardware experts will say that it's often too close to tell, and it's hard to pick a clear winner because Nintendo is so secretive about their hardware.