I have the same converter that Arsenal and Mao linked to: XCM cross battle adapter. Im no expert, but it seems to lag about 10 frames behind my inputs.
The main issue I have with this converter is that it seems to drop special move inputs quite often. For example, when I would input db2 or db4 the in game result would be d2 or d4 respectively. This happens maybe 20% of the time.
I wouldn't recommend using this in a tournament. The lag alone will handcuff you you when playing against characters who can frame trap well (e.g. Johnny Cage). You can still win matches, its just a hell of a lot harder.
At first, I wasn't sure if this problem was the converter or just the way MK9 runs on PS3, but recently I picked up a Qanba dual modded fightstick and it works flawlessly (no lag or dropped specials) on both consoles.
Sorry that I don't have a solution for you, I was searching for a good converter for about 4 months before i caved and bought a dual mod.
Also, Mao's feeling is right on; MK9 does lag at random moments on PS3 when offline. I've never really observed this on 360.