[@Archmage MC]
To be fair, both Superman and Batman are "Mary Sue" characters - they're just able to be labeled as such for different reasons.
Superman, because he's pretty OP - though he wouldn't be considered so on his home planet - and Batman because of his behaviour and backstory.

edit ;; I gotta go, though, so I hope you guys can sort this out. (I'd really leave the decision up to the GM, though.)