If you're a particular fan of Nintendo (Mario, Zelda etc) then I'd say you may well be best off with a Gamecube. After all, SR are doing it for £128.99 and you could probably squeeze a couple of games in for around £200.
The Xbox is one for the 'serious' gamers. Those who want not only multiplayer gaming but ONLINE multiplayer in future. Games like Grand Prix 4, Championship Manager and Midtown Madness 3 makes the console tempting to PC gamers who are fed up with the constant upgrading.
The Xbox is incredible, I love it just as much if not more than my PS2. It's £70 more than a Gamecube though so if it's the Ninty games you like then go for that instead.
Simple as that. The Xbox has four controller ports as opposed to PS2's 2 ports. Because of this, ALL games that have multiplayer will support 4 players. On PS2 this is not always the case, quite a few games only support 2 player.
Multiplayer is the best thing ever. There's nothing quite like beating your mates at something.
Added to that, the broadban aspects. I know that not everyone has broadband, but it's planning ahead. Broadband is getting cheaper all the time, I reckong within a year it'll be affordable for most people.
Again, because it's standard equipment, all games will support it.
The other factor is the DVD player. If you don't have a stand alone player then you should get an Xbox.
The simple fact is that it's higher quality than PS2. No lip synch problems, no green screen problems. It also has Dolby Digital included, so if you have a de-coder then you can enjoy surround sound on all games.
Bascially, for an extra £70 over the GC, you get so much more hardware and so much more potential with the Xbox.
Having said all that, it is all about the games.
Most of the BIG 3rd party titles, Tonty Hawks, Soul Calibur, SSX, FIFA, ISS etc are being released across all platforms. So you need to decided which games are the ones for you. Mario or Halo? PGR or Luigi? etc...