As someone who loves fighting games, but wants to play persona 4 and hasn't yet I'm torn. I don't want to spoil the persona 4 story by playing through the game, but I also really want to get into this game relativity early. So the clincher for me is how is the online; both in terms of stability and player skill level?

It does a relatively good job of matching people of your skill level, so things are pretty mixed right now. There are S rank players that will utterly destroy you and other beginners that you'll do equally against.

When you search for ranked matches you can do a custom search to display the available games and it will show you the skill level of the people. I have seen people with all the grades so there is a good mix if you want that.

If you lose to a pink teddie, it's probably me.

Pretty good, at least for now. The matchmaking is working pretty well, although if you play super early or super late. Ur going to be playing people probably around rank B-C no matter what rank you are.

Online is extremely stable , around 1 in 10 matches has a so so lag but nothing unplayable (unlike Capcom´s fighters) and I always been matched with people around my skill level so go for it duder!!!!

When this game was brand new, I think this game had a greater than average number of bad players compared to other fighting games. That is probably because it attracted people that love Persona 4 but have never played fighting games.
 After you play for a little bit and your rank goes up, the skill level is on par with what you'd expect out of online in any other fighting game though.
 
The net code is really fantastic. When the game first launched, the Xbox version was a bit busted, but they patched that very fast and now it too runs smoothly. Usually even if you match yourself against someone where the game says the connection will be bad, it still actually runs well.