The original XBox used Nvidia hardware, which was basically an early, custom version of the GeForce 3. It had primitive shader technology (compared to the PS3 and 360 graphics chips), but it *did* have programmable shaders.
The Wii's graphics chipset is, basically, an overclocked version of the GC's. The GC didn't have programmable shaders, but it did have some "neato" functionality (some unusual z-buffer texture support, amongst other gizmos). The Wii's chipset is, more or less, just a faster version of the GC's. The original XBox's graphics chipset was primitive to the point of, frankly, not being able to do much more than the fixed function pipeline of the GC/Wii (for any serious game, not a demo), but it *was* programmable. It and the Wii are pretty darn close, in terms of raw polygon/texel performance, unless you wrote some real fancy shaders on the XBox, which would be something the GC/Wii couldn't do, but were pretty slow overall (as compared to modern shaders) -- so fancy shading techniques weren't really used much on the XBox, unless the situation called for it.
The Wii's graphics performance suffers primarily from the fact that the Wii doesn't really have much more graphics memory to utilize than a XBox did, but it beats the socks off the GC. I want to say it has 64M of base RAM, and an additional 24M (+3M I think, embedded on the chip?) of VRAM, whereas the GC had 24M of RAM and, I think only 3M of VRAM. The XBox had 64M of RAM total shared between the CPU and GPU, and likely anywhere from 16-24M of that was typically allocated to the GPU... but that was entirely app dependant. In some situations, the XBox GPU would have both fancier shaders AND more memory, but I think that was typically pretty rare. The CPU needs memory too -- and not in small amounts.
In any case, fixed function pipelines can look decent if you're clever with your resource allocation, but it will never be on par with the X360 or PS3, for a variety of reasons (clock, memory, and shader technology being the main ones). The Wii's GPU (and CPU, really), is on par with the best of the last-gen, no matter how you look at it. Its a little better than the XBox, IMO, but certainly not "2x" better.... "1.5x" better would be the furthest I would take that analogy.
