This is an apples and oranges situation I think. The characters represent different ideas.
Superman has a "soul" we should aspire to have. It's in the name, Nietzsche's Superman is the idea of the perfect human, which is what Superman represents, he does good because it's good to do good. That's his motivation, it may be cookie cutter or uninteresting (to the short sighted) but how many people do you know who do good for no reason at all? What is a man like that like?
Whereas Batman represents something different. He's supposed to be the "drive" that we should aspire to have. He's perfected himself physically and mentally, and as such is able to stand as a peer to a man with the ideal soul. He represents what we could be too. But it's all born of negativity, he did it because of loss, still a fairly cookie cutter motivation, but more "relatable" for lack of a better word.
Batman's "mission" is incredibly short sighted no matter how noble it may be. Most of his foes are incredibly nihilistic individuals and in a sense Batman demonstrates it himself. But look at the Al Ghuls, they recognise that Bruce will squander his fortune, die a pauper and waste his life because at a very fundamental level, he will never rise above his villains. He'll spend his days battling clowns and quizmasters in the mud (until Flashpoint that was his canonical ending, now it's repeatedly cloning himself). In the end, Bruce's greatest achievement will never be the villains he battles, but the people recruited to his cause. He began three generations of people who recognise that as long as they are needed, Batman & Robin will never die.
Superman may have what seems like a more futile "Neverending Battle" his is more hopeful. It's not devoted to one city, it's for everyone. Of all times, cities, creeds. The ability to fight evil at the source, the actions on evil thought. He'll wait until the end of the universe to keep giving people the chance for compassion and redemption, because everybody deserves it.
I know people haven't said it here, but people of cite that Batman is more "relatable" than Superman. Which is at best a half truth. Bruce Wayne is far less "ordinary" than Clark Kent, but Batman is far more "ordinary" than Superman.
Basically what I'm trying to say is, here's my argument for Superman:
And here's Batman:
Superman fights death and Batman fights the impossible. I love that difference.