It’s probably going to be very easy to think that the logical thing for them to do with him is have him face off against Thor again, or even have Enchantress (if she’s in) or Loki brainwash Hulk into an antagonistic force as part of Bruce’s narrative drama yet again.
But I really hope that’s exactly not what they do. Instead they should embrace the unique opportunities that the Asgard setting provides for the character(s).
Think about it, if Thor brings Bruce to Asgard, Bruce is not only in an alien setting with fascinating magic science going on (which should be like being a kid in a candy shop for him), but he’ll also be in a place where the average citizen can probably recover from being punched through a wall (and probably punch each other through walls regularly), and if Bruce were to suddenly snap, there exists warriors and technology of such a caliber that the rampage may actually be subdued before too much collateral damage is suffered.
Asgard could be a place where Bruce feels comfortable in his own skin and can allow himself to feel like he belongs. It can be a home for him.
And if there’s going to be any Hulk vs Thor going on, I’d like Marvel to subvert what one would expect from the fight. Instead of a death match, it could be a sparring match. Think about it, outside of the obligatory rampage scenes, Hulk has been pretty cooperative and intelligent in the Avengers movies. He even operated some Quinjet controls at the end of AoU. I think Hulk is primed for a departure from the animal minded brute that he’s been since the first movie.
So I think Hulk would be capable of expanding his knowledge at this point of his existence (and hopefully will be able to engage in dialogue too). He may also be willing to learn from Thor. Would he be a prized pupil? Not necessarily. What he learns from Thor could be more a crude mimic with the same Hulk flair, but the movie could equip him with some techniques that will serve him well in the final battle.
And besides, with that context, their rematch could be a montage of them gleefully smashing each other’s faces in and then laughing it off later. Such a scene could demonstrate them letting loose in an appropriate fighting area, establishing new feats for the both of them without the baggage of the narrative of Thor having to stop Hulk. Leave the high stakes and desperation to the part of the story where the shit hits the fan and both Thor and Hulk are the underdogs to a larger threat.
And speaking of the final battle, I do understand that it’s part of the Hulk mythos that Bruce be surrounded by tragedy. Unfortunately for him, he’s going to Asgard in a movie called Ragnarok. So Marvel, you want to create drama in Bruce’s arc in Thor 3? Give him happiness and a place in Asgard. Then tear it all away. Leave him broken and angry as he watches his paradise burn to the ground. Such a thing can make him angrier (and sadder) than we’ve ever seen him in the MCU to date.
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(NOTE: All the proposed scenarios are just that. Propositions. These aren’t even very speculative either, since so little is known so far about the plot of Thor: Ragnarok. At least, no in-detail plot synopses have come to my attention yet. So I guess this is all just what I hope we may see.)