I don't think they'd fight, really. Probably just end up realizing it was a misunderstanding over a box of apple caramel doughnuts.
Ok, apparently, I need to clarify this: for all of you from my generation, remember the MTV show "Celebrity Deathmatch"? There, the celebrities would ALWAYS fight to to death. It didn't matter what morals or moral compass the celebrities may or may not have, once they stepped in the Celebrity Deathmatch ring, it was a fight to the death, and that was it. The exceptions to this were few and far-between. For those from Generation Z, remember the game "Mortal Kombat VS DC Universe"? There, the "Kombat Rage" made the DC superheroes throw away their morals so they would fight the Mortal Kombat characters and/or each other. My blog works on similar principles. It doesn't matter what morals the characters may have in canon, once they enter my site, they WILL fight, until the other side is either knocked out or outright killed. Comments such as "X character doesn't kill!" or "X character wouldn't fight!" are NOT valid when discussing the fights in my blog. Call it "Kombat Rage", call it me going by "Celebrity Deathmatch" rules, but in this blog, there WILL be a fight and there WILL be a winner.