Superman falls from the sky after stopping DD. The Hulk catches him while destroying a building. Hulk then punches Bruce and says, "puny Batgod." The masses will lap it up!
Funny you should mention that. I've been playing around in my mind lately how a JL/Avengers movie could happen (aside from WB/DC and Marvel agreeing to it or hell freezing over, whichever comes first) and with the potential Darkseid angle, I imagine that somehow in the aftermath of the battle with Doomsday (weeks/months later), Superman is, after a confrontation with Darkseid, Boom Tubed to Avengers Earth and the first being he runs into is the Hulk still on the run after the evens in
Age of Ultron.
Something like the Boom Tube ports Superman into the Quinjet the Hulk is fleeing in and it crashes, pissing off Hulk. It happens to crash near civilians in a rather remote area. As he gets up, Superman sees terrified people running from a green rage monster . This, after he not too long before fought a gray rage monster.
Of course, the two titans battle it out, with Superman barely winning. In my mind, I have him punching Hulk in solar plexus as Hulk is exhaling, causing him to lose his breath, then Superman grabbing Hulk holding from behind in a kind of reverse bear hug, preventing him from breathing, holding on for dear life as Hulk thrashes around wildly. Eventually, Hulk passes out from lack of oxygen, with Superman seeing him reverting back into Bruce Banner.
Just so happens, the Avengers arrive on the scene, having being tracking the Hulk all this time. They see their ally unconscious on the ground (at least, they hope he's unconscious and not worse) with some stranger in a costume looking over him. You know what comes next--Superman vs the Avengers!
Superman is holding his own, but he is going up against:
Captain America
Thor
Iron Man
Vision
Scarlett Witch
Quicksilver (in my head cannon, he survived)
Black Widow
Hawkeye
However, before long, Batman, Wonder Woman, Aquaman, Cyborg and CW Flash and Green Arrow (hey, I said this is my head cannon) Boom Tube to Avengers Earth to rescue Superman. And of course they see their ally being assailed by a group of costumed characters, so you know what comes next--JLA vs Avengers!
Oh, and Banner wakes up and sees this is a Code Green. Suffice to say, the defecation slams into the oscillation machine.
Somehow, the two groups are in the middle of a game of thrones--er, I mean chess between Darkseid and Thanos. Still working things out in my mind, but there you go.