I hate to ask such a trite question but I wan't to know which version to get. I have a 360, PS3 and PC. I wan't the version that is the most stable online and has the most players. I also have a 360 fight stick (aka a PC fight stick) but was told it's not really a fight stick game. Does the PC version have especially bad Rage Quits or "Slow Computer lag" in matches. I had an awful time with rage quits in the PC version of SF4. Thanks ahead of time!
I play on three versions--360, PS3, Vita. Community is alive and well on the 360 and PS3. You'll probably find an equal amount of players on either console, with perhaps a slight skewing toward the PS3 version. Otherwise, the PC crowd, from what I'm hearing, has encountered a number of matchmaking bugs that impede online playability.
As for "stability," both console versions run really well online. It is important to note, though, that your in-match experience will vary depending on who and where your opponent is. A person from California, for instance, is going to have a tough time playing someone from the UK with anything but the most reliable of moves. And Injustice has a pretty large international following, so you're bound to have a laggy match here and there.
Concerning fightsticks: Injustice, much like Mortal Kombat, is a fighting game very specifically designed to work on a controller. You can certainly use a fightstick and be successful--many players do--but the game has controllers in mind from top to bottom. Though I've really enjoyed the time I've spent with this game using a stick, I'm, without question, more comfortable playing with a controller. And as far as the PS3 vs 360 controller goes, I had some issues with the PS3 controllers reading forward/backward jump inputs incorrectly, and less consequential issues with the 360 controller not recognizing quick directional inputs before special moves (that is, the "down, forwardses" or "back, forwardses" before a face button). It's fair to note here that I've since used the PS4 controller on the PS3 version of Injustice, and that seems in many ways like the ideal controller for the game.
So, to answer your question simply: it's a coinflip between the 360 and PS3 version. It's a great game oozing with content. You won't go wrong either way.
Last time I played, which was on the PS3 not too long ago, the game was still very active. It's a very NetherRealms-y game so I'd bet any fighting game fans who are into the Mortal Kombat style of fighting games will stick with the game for a long time and even when the next big fighting game release comes out the Injustice online scene will still be pretty active.
I can't say how the stability is on the PC or 360 but it's been great on the PS3. I've had no dropped games and lag has almost never been an issue. Oh and like the poster above said the game works perfectly on a normal controller.