They are indeed different and distinct characters, and I wouldn't want to see them written as if they'd both make the same decisions in every situation.
But I'm tired of them being talked about as if they were created by the same creators specifically to be mirror images of each other. And that dark and gritty stories are only allowed for Batman.
Superman came first, and was in fact pretty much an Urban Vigilante all through the year before Batman was created and for awhile after. And when they started writing Super-villains for them, they were initially about the same kinds of super-villains. Batman fought a few Ultra-Humanite knock offs before his Iconic Rouges gallery came along.
People talk about the earlier characters Batman was inspired by a lot, The Bat, The Shadow, Dick Tracey and so on (and my fellow BlackCoatPress fans can trace those back to older lesser known French characters like Judex). But it's forgotten that Superman was first and foremost among them. Kane and Finger were given a mandate to create a second Superman for DC, and Batman's look was simply Kane drawing a Bat themed Mask over a sketch of Superman and then coloring it in differently.
NONE of the dark things about MOS lacked precedent in the Comics. Metropolis had faced similar massive destruction in a number of story-lines, like the Battle with Doomsday, or the Battle for Metropolis story a little latter that ended the Alexander Luthor Jr story-line. And looking back on those comics now often makes me think of 9/11. And Superman comics DID address 9/11 after it happened.
And in the comics Superman has killed the Pocket Universe version of Zod, Doomsday, and the Cyrborg Superman, to name a few. Two of those didn't stay dead but the point remains, when dealing with threats of that level even Superman knows it's suicide not to fight to kill. Cavil in MOS was actually far more reluctant then comics Superman was to kill Henshaw. And killing the Pocket Universe Zod was him carrying out an execution, capital punishment, on already captured enemies. To me that's far less acceptable.
Batman has the luxury of fighting normal humans or occasionally moderately enhanced humans, with the knowledge and ability to do every non lethal take down possible (which is why he can get away with not allowing himself to kill even in situations where a normal person, even a normal LEO would absolutely have to in self defense). Those are luxuries Superman doesn't have when fighting beings on his level or above it.
Golden Age Superman was just as willing to kill ordinary criminals as Golden Age Batman was.