Debuting in 1938 and 1939 respectively, Superman and Batman have always had an implicit correlation. The only reason Batman was even conceived by Bill Finger and Bob Kane was due to DC Comics wanting to create a hero like Superman. Keep in mind this is before there was really a "superhero" genre to draw from, so they seemed similar enough. Ironically, the characters have been re-envisioned over time as diametrically opposed. Superman - the "Blue Boy Scout" - surveys Metropolis, a city that is as much the pinnacle of civilization as he is the pinnacle of heroism. Batman - the "Dark Knight Detective" - prowls Gotham, a slum so corrupt that it warrants having a shadowy vigilante protecting it. They're kinda different. As such, the notion of the two having a conflict with each other has come up several times in the history of the franchises. Despite the ludicrous nature of a physical god fighting a guy in a bat suit, their conflict often extends to physical combat. And boy do the fans love that! Hence why Warner Bros sequel to Man of Steel promises just that; a brawl between the world's greatest heroes. The question is: what reasons would these two have for fighting each other? While the chances of seeing an actual fight is suspect, there is definitely lots of material to draw from in order to ignite this battle of the titans. If you have any other thoughts on potential plot ideas, feel free to add them in the comments!