Should stay ps3. People forget that different versions of each console as it's progressed changes how it functions for the games.
The reason the ps3 lags sometime is because it heated up faster, much faster, than the 360 and causes it to do so more often. However this is still from the FAT ps3 days. The newer systems very rarely do it, and when they do it's naturally happening in a tournament with a million bodies and systems and monitors all on at once. The 360 was built better that way, and ironically has gotten worse over it's different versions.
In terms of specific games. CAPCOM games were specifically called out because they were the big ones. SF4 has been proven to have the 2 frame latency, MvC3 is proven to have randomly dropped framed and the same lag. Even 3S HD had it for some reason. Their design flaws are what cause it though, not the system. Still, it's enough reason to make it 360.
Blazblue, P4a and GGAC+ are all fine though, hell some say BB is better on PS3 even though i don't think there was any test on that.
Tekken and Soul Calibur are both PS3 ran because other than the load times between matches, it is still flawless IN GAME.
Take that with a major chunk of those TTT2, SC, BB and GG scenes being pad players, it's a no brainer it's on PS3.
Same with MK9, and it should be the same with Injustice.
The only real argument with Injustice is the Controller Config glitch, which only happens on PS3. But again that because they designed the game for 360 Profiles, and PS3 only has 1 profile at a time.
Either way though, there is gonna be a lot of noise coming from the side that wanted the losing console. But after a time it should either die down or it'll die when the game dies.