Ok, lets see...
GC VS. PS2
Gamecube
Games I own:
Metroid Prime
Mario Sunshine
Star Crap Adventures
SSBM
Eternal Darkness
Animal Crossing
PS2
Games that I own:
FFX
Kingdom Hearts
Suikoden 3
GTA3
GTA: VC
Now lets see...
GTA3 and GTA:VC aren't that great too me... Sorry, just an opinion. I mean, this wasn't the reason I bought a PS2...
I mainly bought a PS2 for the RPGs... And my favorite PS2 games are those 3 RPGs I own...
On the other hand, we have the Gamecube.
Okay, so let's compare the genres.
Platformer/Adventure:
Super Mario Sunshine... I liked Mario more than Sly and Ratchet... Mario is my main man when it comes to adventure titles. SMS is loads of fun.
First Person Shooter/FPA:
Metroid Prime... enough said...
RPGs:
Here's where the bomb drops down... Here's where PS2 kicks Nintendo's non-story oriented ass very hard!
SIM/Strategy:
Well... PS2 barely has SIM kind of games... But Nintendo has Animal Crossing... PS2 will get Sims but I don't like Sims much because after I made $2,000,000 on my PC version of SIMs, I got very bored of the game. On the other hand, I don't enjoy Animal Crossing much either... Like it or not, this genre bores me to death. So I'll go with Nintendo on this one.
Sports:
...Oh boy. My most hated genre. yes, sports. You guys wanna know my most hated developer? Well, I think I wont say it since many people like the people behind NBA Live.... Why do I hate them you ask? Sport games are way out of my league and EA sport games are the ONLY games my friends play... So seeing that my friends don't have the slightest clue about the gaming industry, (yes, they don't know what or who rare and Square are... They call FF7 gay since you "stop and fight") I'd rather not talk about it... PS2 reigns supreme on this catergory...
Personally, I like my PS2 better just because of the RPGs... But guess what? I choose Gamecube for a valid reason. I think Nintendo deserves my pick since all their good games are their 1st party games unlike Sony's 3rd partry support. I mean, let's face it, Sony can't create a game that can match up to Nintendo's. My point is that Sony is a publisher and not a developer while Nintendo is both!
Now I am aware that this is favorite consoles we're talking about but, I think the Gamecube is an overall better console than PS2. But I still like my PS2 better just because of the RPGs.
Play Suikoden III, FFX, and Kingdom Hearts and you'll know what I am saying.