if you're asking how is the PS2 network performance, the answer is so-so. it depends on the developer. for instance, there are flawless online games (madden/ncaa) where even if you are on 56k you get a smooth, lag-free performance.
then there are games with TERRIBLE lag and bad performance overall (MVP baseball).
so, to answer your question, the ps2 is good online, but not great. it all depends on the game.