Superman / Batman

Much of the distance is in power discrepancy. Superman can move faster then the speed of light. He is literally impossible to damage in any physical way-only magic and kryptonite affect him. He has nearly unlimited strength-he has moved planets. He never tires and he has an array of other weapons. His heat vision can melt steel, he can freeze nearly anything with ice breath, his super breath can make airplanes stop in midair, and he can fly. He is nearly unstoppable.

Batman has no powers-he is merely a man. But Batman is honed to the phyisical and mental peak. He is one of the three smartest men in the DCU, along with Mr. Terrific and Lex Luthor. He also is one of the greatest martial artists alive, and he has loads of technology and money, including tools like Batarangs. He is a master tactician. This is why they need to take different approaches.

Although both have a different method (and they are often at odds), they team up all the time, and together, are one of the greatest team-ups in history-Superman/Batman.

Adventures

The "team" started when President Lex Luthor declared both heroes enemies of the state and put huge warrants out for their arrest. His reason-a kryptonite asteroid is heading towards Earth, and Luthor blames Superman. He offers a 1,000,000,000 bounty for the two heroes-so every hunter in the country-plus many heroes and villains-are suddenly gunning for Superman and Batman. Superman confronts Luthor in the Oval Office and nearly kills him, and Batman lets him-but Kal-El steps aside and spares Luthor. They meanwhile have to find a solution to the asteroid problem-and the solution is the new Toyman, who builds a spacecraft that can destroy the asteroid. This poses a problem for Luthor-so he takes drastic measures. He injects himself with Venom and synthetic Kryptonite, dons a battle suit from Apokolips and tries to kill Superman and Batman himself. He is defeated and exposed-and it costs Lex Luthor the presidency. This is documented in Superman/Batman # 1-6.

They also saw the introduction of someone important in Superman's life-another Kryptonian. The kryptonite asteroid lands when Batman detects life on it, and Kara Zor-El-Superman's cousin-is inside the ship. She becomes the new Supergirl. Batman is (of course) suspicious-he thinks it was too coincidental for another Kryptonian to pop in now. It doesn't much matter, for Wonder Woman abducted the girl to Themiscyra for training. All of this, of course, attracts the attention of Evil Incarnate-Darkseid. He wrecks Themiscyra and attempts to steal Supergirl so she can lead his Female Furies. Batman and Superman stop the evil Lord of Apokolips, and Superman angrily throws him into the Source Wall. Supergirl is saved. This is documented in Superman/Batman # 8-13.

Later, Mr. Mxyzptlk battles the Joker, who has tricked Bat-Mite out of his powers, using other characters as their pawns (much like what he did to Mxyzptlk in Emperor Joker). Superman and Batman fight a team of superheroes from an alternate universe called the Maximums (a analogue of Marvel Comics' Avengers series, more specifically their incarnations from the Ultimate universe, the Ultimates). Keeping the bargain he made in issues 8-13, Superman frees Darkseid from the Source Wall, and, double-crossed by Darkseid, becomes trapped in the Source Wall instead. Recruited by Bizarro, multiple versions of Supergirl rescue Superman from the Source Wall before they are all transported to an arena. There, they fight Darkseid, Lex Luthor, and evil versions of Superboy and Supergirl in a battle that involves versions of Supermen and Batmen from many different realities. Bat-Mite escapes, and the two imps tie up all the loose ends and return all the participants to their point of origin.