Not quite sure how this would play out, but basically:
Batman wins the North-East and the old Rockefeller Republican states due to his roots. In New York, his roots as an established businessman, Upstate Conservative voters, and the Rudy Giuliani voters put Batman over the top. He wins the Libertarian West due to his anti-establishment-ness, wins Utah, Alabama, and Mississippi due to the fact that Superman has God powers, which can't be good for the religious folk. He wins Texas with his business-friendly economic plans.
Superman wins the rural Mid-West, the Southern parts of the Rust Belt who aren't going to vote for that yankee billionaire, the military states due to his faithful service to the US, and the Pacific West due to an overall more tolerante yet at the same time "All-American" message.
It's tricky as Libertarians could label either of the candidates as "fascists". Urban areas might vote Batman due to the fact that he's cleaning up the street, but he's also a source of fear. That's why DC is a tossup.
Blue: Batman (R-NY)-276 electoral votesRed: Superman (D-KS)-159 electoral votesNOTA: 3 electoral votes