What's wrong with the GC?
I've got both PS2 and GC. No XBox and no intention of ever getting one if for no other reason than principle.
I honestly play the GC far more than the PS2. I've only got Vice City and GT3 on the PS2, I've got Metroid Prime, Rogue Leader Rogue Squadron II, Pikmin, Timesplitters2, and Robotech Battlecry for the GC. Prime is definitely one badass single player game.
There are a lot more titles for the PS2 but the very vast majority don't appeal to me. There are tons of shitty games and just flat uninteresting games for the PS2 when compared to my taste. Of course this goes for all consoles, but there is more that appeals to me on the GC. I would say that it really depends on your tastes in games for which to get.
Here's my breakdown of some differences in the PS2 and GC:
Controllers: PS2 analog is more smooth than the GC C stick analog, the C stick (little yellow one) is VERY sensitive and I have yet to see a game that allows me to adjust its sensitivity, HOWEVER the GC controller is faster than the PS2 controller; translation, it's easier to be very precise with the PS2 for driving/aiming but it's easier to move fast with the GC. GC controller is more comfortable than the PS2 controller and is cheaper to buy. For games that are available on multiple consoles, the controller can be very important.
Graphics: Hands down the GC beats the PS2. XBox beats the GC in some ways. For games that are available on all 3, you'll find best graphics on GC or XB depending on tatses in graphics. I'm not sure that the PS2 supports component video but the GC does (must buy cable from Nintendo directly, although I believe Monster now sells one). Unless you have a high end receiver, though, with the XB and GC and maybe DVD you'll maybe have too many component sources anyways.
Sound: I don't run a fancy surround system yet (will next month), but I think they are ranked as XB #1, GC #2, and PS2 #3.
Video adjustment: The GC has an adjustment allowing you to shift the video left or right on the console. Some games support shifting as well (such as VC and Prime), however PS2 does not support this at the console level. GT3 has a big band on the left that gets unused on my TV due to the input source and TV not agreeing.....GC games don't have this problem.
Load times: GC loads much faster than PS2 for same titles. For TS2 we're talking 5 versus 20-30 seconds for levels.
Titles: There are very strong PS2 only and GC only games, just like XB. For the GC I personally like Pikmin, Prime, Rogue Leader as being very nice GC-exclusive games, consequently 1 player games. For the PS2 I think GT3 (and probably 4), GTA 3 and VC, and Socom are some of the nicest exclusive titles.
My personal recommendation: Pick the one with the titles you are about the most. If that's not a biggie then try them both and pick the one with the controller you prefer the most. If you still can't decide, take the Cube cuz it's newer, smaller, prettier, and sounds better.
Anyhoo, I hope it's more helpful than the usual "buy this one" or "buy that one" responses.
EDIT BELOW:
More on controllers: GC natively supports 4 controllers and many multi-player games also support 4. PS2 you've gotta shell out extra cash for up to 4 controllers and many (if not most) multi-player games only support 2 players anyways.
Networking: PS2 wins over GC in this department. I'm not sure how the networking of the PS2 compares to the XB, but as far as I've seen the GC has no current network it'll operate on.
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