This is a simple question
In choosing between the Xbox and the PS2 (or any other console, for that matter) there are two factors. First, the system.
There is no way (bear with me on this) in which the PS2 is better than the Xbox, technically. Of the three new generation machines, the Xbox is the most powerful, though the difference between it and the GameCube is sometimes hard to tell. Graphically, Xbox games shine, and PS2 games look a little muddy and jaggy by comparison. The hard drive is a nice feature, simplifying things like save games, though hasn't been as revolutionary as it should be, due to poor implementation in games. The support for DVDs out of the box is nice, but flawed. No progressive scan on DVDs for absolutely no reason, and the need to buy a remote is a mixed blessing at best.
BUT the area where the PS2 shines is in games. There's a lot of crap out there, don't get me wrong, but the sheer volume of PS2 games means you WILL find some you like, and the high number of PS2s out there means that most games are released for the PS2, though if there is a multi-platform game, the PS2 is often the worst. Xbox is not necessarily such a definite. Not that there aren't some great games on Xbox, but fans of specific genres (esp fighting games, or RPGs) should seriously think about which platform best caters to their needs.
My advice: Take a look at the games that are out now, or coming out before the end of the year, and decide accordingly. My PERSONAL preference is for the Xbox, though it needs more killer titles. The graphics of the PS2 bother me a bit, and the games don't really enthuse me. Not that there aren't games I want on it, but not enough to buy the console.
Anyway, my two cents.