My kids have the PS-2, X-box, and a Gamecube. Not really sure how that happened, the grandparents spoil them too much. I have played them all, and I can give you a 40-year old's perspective on 'em.
The kids tend to play the X-box the most, I prefer the PS-2. Mostly because there are a couple of games they have for the PS-2 that I really enjoy (Simpsons Hit and Run, etc). There are lots of grown-up games (RPGs, flight simulators, etc) on the X-box, but most of those are available on the PC too and I prefer playing them on the PC. (Some of them are so violent and have such "mature language" like GTA-San Andreas that I wouldn't be comfortable letting kids play them at all).
Gamecube is behind the pack in terms of power, the games are usually the worst of the lot too. The Nintendo franchise is long on kiddy games IMHO, the only ones that hold my interest are the Zelda series.
The X-box has a better DVD-playback than our PS-2, on the PS-2 dark scenes become almost black and tough to see detail. The X-box plays back DVD's as good as most dedicated players.
Something that has surprised me is how fast the younger kids lose interest in the "big games" but continue to return time and again to franchise formula crap. Based on my kids and the Cub Scouts I've been around for years, the average kid spends more time playing Pokemon, Yu-gi-Oh, and Dragonball Z type games than everything else combined. I find those games absolutely mind-numbingly boring, but kids play them for hours on end.

All of the three major systems have pretty much identical titles in those arenas, so no matter what you buy your kids will find stuff they like to play.
But if YOU want to play, I'd say #1 = X-box, #2 = PS-2. Avoid Gamecube
