I definitly think the Gamecube has a brighter future than the XBox does.
So many of the biggest third-party developers have gotten close to Nintendo recently. There are so many joint-venture projects in the works. I think Nintendo's strategy of forging real relationships with developers will, in the long-run, do a lot more for it than MS's practice of simply paying off developers for exclusives.
Of course the XBox's complete failure in Japan will prevent most Japanese developers (which are still, by far, the most important developers to have on your team) from supporting it too strongly. This is what will REALLY hurt MS in the long-term.
Of course, it goes without saying that Nintendo has superior first/second party support over MS. So if it really does gain the upper-hand for third-party support (and I'm confident it will), there's no reason Nintendo won't be able to leave MS in a distant third place. It may take a while though. It wasn't until the very end of the SNES's run that it gained a notable lead over the Genesis. I think we'll see something similar happen with the Gamecube.