On ps2 you just need the network adapter (40$) to get online. It isnt as cool as XBOX live but if the game has online capability you can play against other people online.
Xbox can be used after modding if you've got it set up correctly. Ive got the xecuter2 modchip for my xbox, Ive got switches running from the front of the xbox to the modchip so I can turn the modchip on/off. If you go on xbox live with the modchip on you will be banned. Also if you've got an upgraded hard drive you will need to lock it (it needs to be a lockable drive) for the xbox dashboard and xbox live to work.
The xbox is leaps and bounds above the ps2 as far as modding goes.. my xbox took over as my tv pc.. Ive got GentooX linux on it to browse the web, I watch all my d/l'd movies on it, and you can back the games up to the hd.