Xbox on-line is accomplished via joining Xbox live. The caveat is you must have broadband. My exprience with it has been great. Performance is consistent with no lag. I attribute this to a more controlled network due to xbox live. This also provides a community type atmosphere for communicating, downloads, updates and the like. There is a 50 dollar annual fee for unlimited gaming and access.
PS2 on line is accomplished via the game publishers itself. It supports dial up as well. I would imagine that due to the variances in internet access, server hosting and such, that perforamce and lag would vary greatly. Not sure if the live on PS2 suuports downloads, updates and chat. My understanding is there is no fee. Perhaps someone who has used PS2 online can chime in.
Of the two, Xbox live has achieved more success in establishing a more solid on-line foundation, from various sources I have read. I don't think PS2 has as many titles for on-line play as Xbox.
I can say from experience that the Xbox is the best for online so far. With the addition of a friends list not only in each game, but in the dashboard as well and the ability to use your PC to see who on your friends list is playing online is an excellent feature.
As well, the voice chat is flawless as is inviting other people off your friends list to games.
And, their are more variety of cooler online games on Xbox as well.
PS2's main stay for online are all EA games as well as an excellent SOCOM II. But, the online features in SOCOM II were developed by those who developed Xbox Lives online features (e.g. friends list, in-game invite etc...).
Anyhow, if you pay for the Xbox Live kit, you get the service, 2 games and the headset as well. Can't go wrong my friend.