Superman encompasses those that believe in the virtues of an ultimate super hero. They idealize superman for being the strongest, indestructible, and virtually unbeatable, while maintaining an air of modesty and morality. Superman appeals to those that feel that justice and morality are unyielding and unstoppable, and such is reflected in superman as being the "perfect" superhero.
Batman encompasses the other end of the spectrum. while still being a "hero", Batman is bound by human physical limits, and instead relies on his intellect and skills to battle his enemies. he is not as morally bound as Superman, and often crosses an ethical line that superman would not. he is the quintessential "brains over brawn", and such is his appeal to those that feel that a lack of "super powers" does not keep you from being a badass hero. while having no way to match any of supermans physical abilities, and being the only original Justice league member without super powers, Batman is generally characterized as the one person that is able to beat superman.
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