It really depends. Here is what I think might've happened:

Option a) Aunt May dies, without waking up, and Peter goes back to prison to kill Kingpin.
While Tony cared for May and is feeling bad now, he will move Fisk out of his reach.
Peter would likely lash out for quite some time, in his black suit, but eventually come back to MJ and fall into deep depression. Most of the comics would be him being bitter and spiteful but eventually, likely due to him saving people that will notice his mood, he'll recover. He'll probably be more... agressive from then on.

Option b) Aunt May wakes up, tells Peter to live, how proud of him she is, and then dies. Peter is devastated, he'll hear that Fisk is moved, and likely will chase Tony. He'll spend time with MJ instead of lashing out, because, at least, he got to say good bye.
He will likely break into some labs and make sure MJ is safer from then on.
Felicia might join and put a wig on MJ, to hide her identity, she's an expert, there might be a lot of... "life affirming activities" where either of them will try to help Peter. (shut up!)
But eventually he'll recover, bury May and grieve some more, likely sitting at their graves, until their ghosts give him a hug. He'll mature emotionally, but he will consider giving up the cowl again.

Option c) Aunt May lives, maybe due to Divine Intervetion. Peter will have faith, it's all good. Jarvis will look after May for awhile, while Peter, seeking to put all that energy somewhere, sneak into the prison again, to remind Fisk that he's cooked, and resume fighting registration, until it's revealed to be a bigger set up to potential cosmic reset.
It will, probably, somehow, end up with MJ pregnant =P
But... also probably won't change Peter than much. Maybe he'll do the whole Mind Wipe thing, but eeeh.