I have both & never use the Xbox. Both are pretty cheap now, hit ebay and if you're lucky you'll find a few bargains.
I'm guessing that it's easier to get ahold of downloaded games for the Xbox, because of the hard drive... although chipping it may cause problems when you want to use Xbox live. I'm sure that someone here knows more about that because I know virtually nothing.

None of my machines are chipped and I don't use copied games - again, hit ebay and you'll find some good prices on games if you don't want to risk problems with the online gaming service. You can also pick up chipped machines with like 100 games if you're lucky enough to look at the right time.
In terms of sheer gaming experience and nothing else, PS2 vs. XBOX, I'd say that PS2 completely owns, without any hesitation whatsoever.
In terms of downloaded games... Xbox.