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The reasons for this are many, and I'll try to explain some of them for you.
Firstly, I like Nintendo games. I've had a NES, a SNES, an N64 and a Gameboy. Nintendo make games that I enjoy, so I can hope for more of the same on the GAMECUBE. These games will also feature some off the characters that I have grown rather fond of in all my years of gaming, such as Mario and Luigi, Donkey Kong, and Zelda.
Secondly Nintendo are promising innovation with GAMECUBE games. This seems quite apparent in what I've seen so far of the games. Pikmin seems to be a rather original concept for a console game. Luigi's Mansion is very different to 'Mario' games too, and seems to be to be much like 'Ghostbusters'!
Thirdly Nintendo have a number of strong second party developers producing games of a high quality for them. Rare will bring the next Perfect Dark game, Donkey Kong Racing, the Zelda-esque Star Fox Adventures and original games like Kameo. Retro Studios are dealing with the Metroid license, and are also developing Raven Blade, a very promising looking RPG, and a racer. Silicon Knights are also making titles that will appeal to an older generation of gamer, such as Eternal Darkness, and Too Human.
Fourthly, Nintendo have strong 3rd party support this time. Sega are backing them (as well as Xbox and PS2) with some strong games. THQ have 15 titles to launch next year on the 'CUBE, including WWF Wrestlemania, EA will bring their sports titles, Acclaim and Capcom are also working on big, big games.
Finally, the GAMECUBE is affordable. It's likely to be around half (and no more than two thirds) of the price of the Xbox.
I have yet to see anything on the Xbox that impresses me in the way that the GAMECUBE does, so it's Nintendo all the way for me!
Microsoft wait til someone else has tested it and try to steal it....
Anyway I'm looking forward to Pikmin! It looks kinda strange but I like strange games!
The Gamecube will be well better than the Xbox because the gamecube will have quality game makers behind it such as rare and nintendo themselves and because the XBox is microsofts first games console they have no established games producers behind them, only themselves and everybody knows how bad microsoft games are. So if u want a games console with excellent games and lets face it thats the only objective of a games console, you have too pick Gamecube because everything Nintendo makes is quality and from what I've heard the XBox is going to sac mice. So get ur butt into gear and think sense, Gamecube or Xbox?, don't make me laugh.
And to be honest, neither console has shown off many great games. Of course, Ninty have mario/zelda/metroid, and if you're a big fan (like me) you may consider getting it on this basis. However, beyond this, there is little news on games, and you'l have to wait till reviews start coming out. I'd recommend getting EDGE magazine for an unbiased opinion on all the consoles, and very comprehensice reviews.
Sonic
Gamecube out of them two definatly, but there's still another 2 consoles that your haven't mentioned.