I think you should go for the PS2 if you are more into platformers like Ratchet and Clank and the Xbox if you are more into action games like Halo. The rest of the genres are the same on both consoles. So, it's a matter of personal choice.
Also, don't listen to people who say you should buy the PS2 as it has a huge library of games coz you aren't gonna buy each and every game available for the PS2, only the good ones. So check out the games available for both consoles and buy that console whose games appeal to you the most. In my case it was the Xbox.
The reasons why I bought the Xbox are as follows:
a) Plethora of quality games specially action, FPS and RPGs like Halo 1 & 2, Fable, KOTOR I & II, Ninja Gaiden (tell me games exclusive to the PS2 that can match NG or Halo, and no DMC and Killzone don't even come close) etc.
b) Better graphics and sound quality.
c) Presence of a hard drive which eliminates the need of memory cards unlike the PS2 (which BTW aren't cheap and have a tendency to get corrupted). I have never had to delete a single game save ever on the Xbox. Heck, I still have the saves of games that I don't have with me anymore. Also, you can store music on the hard drive and listen to them in game. All this and I still have 4 GB left. The hard drive also makes loading of games much faster. Sample this, GTA:VC takes 90 secs and 9 secs to load on the PS2 and the Xbox respectively.
d) The crazy stuff you can do with a modded Xbox. Install a bigger Hard Drive, run linux, install XBMC to turn your xbox into a complete Media Center etc. Just check out xbox-scene.com.
e) Halo...period
If you want more details to help you, check out the following links for the reviews of the consoles on GameSpot.
Xbox
*hardware.gamespot.com/Microsoft-Xbox-9399-O-4-4?tag=gs_lnav_whatisxbox
Playstation 2
*hardware.gamespot.com/Sony-PlayStation-2-9398-O-4-4
Personally, I wouldn't buy a console at this time because their Next-Gen versions are due out soon (atleast the next version of the Xbox is).