I have a PS2 and a Gamecube, both which I equally enjoy using. However, in the long run, I have a feeling that either Gamecube or X-Box will be the first to fall. My reasons for this is quite simpe.
Gamecube: Since most gamers these days are teens and young adults, it's highly unlikely they'll be playing childish games that are release to Gamecube. I mean Super Mario was the thing back at the NES era but now people want action shoot 'em up, Bang-bang-bang games. As far as I know, Gamecube doesn't have a lot of those types of games to offer.
X-Box: X-Box was a great hit in what? The first few months of its release? It's still pretty good but it's multiplayer system is only good for those broadband users out there. The game console was quite expensive when it first came out but now, with the Christmas coming, it dropped down to a very cheap price. However, most people would chose PS2 (note I said [I]most[/I]) and not X-Box since they know there are more games out of PS2 and it also can play previous Playstation games.
Conclusion: In my opinion, X-Box won't be the first to fall, most likely Gamecube. I don't know why but that's how I see it. Gamecube just can't compete with these two game consoles.