Xbl generally has a superior matchmaking service with a somewhat higher level skill base, since the majority of the fighting game community is on xbox. That being said, there’s still good competition to be found on ps3, plus the online service is free for PS3.
Most tournaments use xboxs, with the notable exception of Evo, which has always used PS3. Your best bet is to check with your local tournament scene and see what they’re running on, and you should follow suit, so that you have an offline setting in which you can test your skills that you’ve honed back home and online.
As far as lag goes, that depends entirely on your internet connection and how well you’ve set up your port forwarding system. Unfortunately, unless you live in Europe or Japan, the internet service won’t be identical to the offline experience, and lag will play a factor in your matches.
Also there are timing differences between the xbox and ps3, not to mention input delay depending on which monitor you’re using. These differences are fairly negligible until you start travelling to different offline events that use a different setup than what you have at home, where you’ll begin to feel these slight delays that vary by a few frames.