I picked up both a GC and an Xbox within a week of each other and have about 10 games for each.
Gamecube is hands down my favorite. If you like sports or racing it's the wrong system, but for everything else it's great.
I love Mario Sunshine and Luigi, the originality is great.
Rallisport Challenge for the Xbox is awesome, but I feel that Sega GT and Project Gotham are both pretty lacking. No analog speed/brakes in Sega GT, and the graphics aren't anything special in either.
I've been far more impressed with what I've seen on the Gamecube graphics wise. The lighting and effects in Luigi are fantastic. That may change when I get Splitner Cell tomorrow though.
I love the feel of the GC controller, and the layout (although not having 8 buttons or the normal 6 layout is bad for fighters). They should have added a Z button on the left side.
The Xbox controller kinda sucks (S version). The grips are too short, and the black and white buttons need to be raised, not indented, I can't hit them. The select and start buttons need to be in the middle, or need to be reversed.
The GC controller is lacking in the rumble department. I thought it was great...until I got the Xbox. Holy freaking cow, now that's rumble! Microsoft hit the nail on the head with that design, it's perfect. In Rallisport Challenge the feedback is great and you can really tell how the car is handling. I've been blown away with it. It even makes the controller rattle sometimes because it vibrates so much.