I have all 3 as well and I would HIGHLY recommend the PS2 over the XBox for sure (and in the end probably even over the Gamecube as well).
The thing is, Xbox is the most powerful hands-down. However, in my opinion, PS2 has the best games PLUS you get the whole PS1 library which has some amazing games on it too. If Xbox weren't by MS, it would have been dead by now, but MS has the resources to keep it going (despite the tons of money they lose on it).
I might have said Gamecube prior to the summer, but after seeing Nintendo's new "strategy" at E3 i.e., worthless GC-GBA link-up, I have lost serious faith in Nintendo.
Also, while I'll admit it's not as bad as it was with Nintendo 64 - Gamecube is still primarily a 1st party machine. Nintendo really needs to work on getting the amazing 3rd party support they had in the SNES days.
In my opinion, PS2 has become the Super Nintendo of today, and we all know that Super Nintendo was the sh*t!
So . . . in closing, buy a Gameboy Advance for that old school gaming you really need, but if you must buy either a PS2 or Xbox, you will get 10000x your money's worth if you go with PS2, despite it's processing and graphics inferiority.