Which is better? Well, in terms of capabilities and features, the XBOX is far away the superior. Its simply no contest.
*The XBOX has a hard drive. You save your games to this hard drive. You'll never run out of space. Hence, you will never need a memory card. You can also story music on this hard drive, if you wish.
*The XBOX can copy and burn CD's for you.
*The XBOX has four controller ports, twice as many as the PS2.
*The XBOX Live is reported to be far superior to the PS2 online multiplayer system.
*Both will play DVD's for you. They are cheap DVD players, though.
*As already mentioned, the XBOX is a considerably more powerful machine.
Most titles these days are multi-platform, but there still exist some exclusive titles. Sometimes its because XBOX/GC games are simply to much for the PS2 too to handle (they are usually the games that make you gasp and say "wow"), other times it's because they're big "franchise" titles. In your selection you should consider which titles you wish access to most.
They only "advantages" the playstation might have is price and a few nice exclusive titles.
I own both, BTW.