As usual, it all depends on what games you like to play. But for the most part, I have to go with PS2. Between the summer of 2003 and the summer of 2004, I think Xbox is a clear winner, but overall, the PS2 still has the obvious edge.
Look at it closely-
The PS2 has almost ALL video game genres covered. You will not see JRPG's on the Xbox, you won't see strategy games on the Xbox, there really aren't any exclusive fighters or platformers on Xbox that are worth playing, and you won't see any rhythm/dance titles on Xbox, either (I believe it just got its first one, DDR). When you can list 35+ RPG's, Virtua Fighter 4, Ratchet and Clank/R&C: GC, Jak and Daxter/Jak II, Dynasty Tactics, Romance of the Three Kingdoms VII, VIII, Disgaea, La Pucelle Tactics, Ring of Red, Amplitude, Gitaroo-Man, Frequency, etc....all on PS2, and with no representatives on Xbox, that says something about each system's diversity.
If you're only into FPS, Western RPGs, and action/sports games, than Xbox is probably the system for you. It also has, 95% of the time, the best version of multi-platform titles. It's why I own one. But there's also a reason why I have 36 PS2 games and 16 Xbox games...there's simply so much more to choose from on the PS2, and I'm a HUGE RPG fan. Add in top "AAA" games like Final Fantasy X, Devil May Cry, Onimusha 2/3, Ratchet and Clank/R&C: GC, Gran Turismo 3, Ace Combat 4, Kingdom Hearts, Amplitude, Jak and Daxter/Jak II, Suikoden III, Xenosaga, Red Faction, Silent Hill 3, Soul Reaver 2, Virtua Fighter 4, etc., and it's an easy choice for me.
I could never do without some of the choice titles in my Xbox collection, though. Chronicles of Riddick, Halo, Top Spin, Ninja Gaiden, and both Splinter Cells (best played on Xbox), are more than enough to make me want to keep the system.