Pretty straightforward, is there still a really fun and competitive community around this game? I don't have a ps3 right now but I will in a few months time and would really like to get back into it even if I can just have some matches with people around here.
The GameFAQs forum for this game is not that active. It's probably better to look at the official forums or psabr.boards.net if you're looking for tournaments.
Anywya, there exists a competitve 1v1 scene, but it's probably pretty small compared to other games.
A couple of offline tournaments have taken place. The most recent one in Toronto and an upcoming one in Texas.
Online tournaments are held frequently enough. You an already see a couple of them when looking on the front page of the officials: http://community.us.playstation.com/t5/PlayStation-All-Stars-Battle/bd-p/24861
Besides that Fight club matches are streamed almost every day of the week. For a schedule you can look here: http://community.us.playstation.com/t5/PlayStation-All-Stars-Battle/PSA-Streams-amp-Fight-Club-Directory/td-p/41985217