#3. Batman Benefits from the Shared Universe
The most crippling factor in mainstream comics is the shared universe. Hamlet never had to explain why Sherlock Holmes couldn't just solve the royal murder, and his play didn't end early because someone wanted to restart the universe to make Superman and Batman interesting again. (In fact, think about how badly you'd have to screw up to make that necessary!) But every crisis in DC has to explain how problems exist despite Superman's existence, and likewise, Superman has to stand around like a Kryptonian statue so that everyone else doesn't feel useless. Every time he stands next to Green Arrow, it just embarrasses both of them.
"I'm holding back the unstoppable pure energy beam! Quick, Oliver, use that bit of wood and string you carry!"
Putting super-powerful characters in a shared universe is like freezing them in amber -- you need a specialized team of experts to let them do anything afterward, and it never works right. Superman can knock the moon out of orbit, but he can't so much as punch out Captain Cold without first checking if the Flash wants to spend another four issues failing to realize that thermodynamics clearly don't apply to him.
Curses, if only I had a power that made me better at avoiding things!
But Batman benefits from other heroes so much that they made an entire series about it. The Brave and the Bold is all about an unpowered human keeping up with (and often outright embarrassing) heroes who can unmake mountains. Every time he meets another hero, the question is "How could he beat them?" a question he's already answered so hard that he once took out the entire Justice League by accident.
Either that or he's the best at partying (because he's the Best At Everything).
Sometimes it's by making Kryptonian skin transparent to the solar radiation it needs, other times it's by realizing that a magic ring doesn't prevent someone from being an asshole.
The Green Lantern Corps gives out gaudy rings like Christmas crackers.
#2. Batman Teaches a Better Message
Another odd point for a man dressed as a giant domme-animal. But Batman's core message is that anyone can reach for the stars if they're kicked in the ass at escape velocity.
Simultaneously the worst and best motivational seminar ever conducted.
His whole point is being better than superheroes despite not having superpowers. His lesson is "Life sucks, wear a helmet, then install bat-ears and sonar technology into the helmet so you can track life down and make it swallow its own sucking tongue." Batman worked and learned to be everything he is, while Clark Kent has to pretend he wasn't just born better than everyone else. Sure, Bruce inherited infinite dollars, but that's only because a janitor of vengeance working overtime to afford moparangs isn't as cool. Batman penniless and alone kicks just as much ass (and has been in at least three story arcs). Superman is meant to represent everything humanity can strive to be, the pinnacle of selflessness, but he only reinforces the lesson "If you weren't born to the right parents, you are shit out of luck." Which is a weird angle for someone meant to embody the American dream.
Any non-U.S. citizens looking at this image have just been naturalized.
#1. Batman Would Lose the Fight
This debate always devolves to the playground level of "Who would win in a fight?" and this ultimate showdown proves that Batman is the better character. Because everyone knows the answer. It's obvious just looking at the two of them. He's the Goddamn Batman.
And he would lose. That's what makes him better.
"He always outwits me, so if I pull out his wits he'll be helpless!"
Batman faces the impossible and he makes a plan for it. Batman hurting Superman is always treated as a big scary deal, but Batman being hurt is business as usual, and he fights on anyway. His plans are the only case of a rich white man hunting an alien that humanity can be proud of. He knows more about the obsessive minutiae of the comics universe than the people arguing that he'd win, and he knows better, and he still does it.
In Soviet Russia, no memetic reversal, Batman STILL punches you.
A room full of Kryptonite nano-fog and power armor cursed with ancient magic doesn't work when your enemy can drop the moon onto whichever continent it's built on. Batman only gets a chance because Superman refuses to kill him, and is doomed because the same handicap hurts him far more. He won't kill, so the instant the sun lamps fail, the Kryptonite laser is out of alignment, the power-damping chains are cut, they're out of the gas-filled pipe under the city of innocents, the serum wears off, or anything at all is one micron less than perfect, he's toast. The second law of thermodynamics guarantees Super-iority. But facing impossible challenges is true heroism.
The most famous Bat-victory of all time, The Dark Knight Returns, was based on Superman being weakened from half-saving America from an atomic bomb, agreeing not to cripple Batman with laser vision, meeting at a time and place of Bruce's choosing, agreeing not to cripple etc. etc., walking into punching range of Bat's incredibly obvious machine, ANTCBWLV ... and even then Batman's best plan was "Die at the one moment it looks like I'm winning so he can't call takebacks."
And this is still the second-greatest moment in comics.
Supporting Superman because he'd win is like supporting a nuclear warhead because it would beat your smartphone -- of course it would, but which is more interesting? Which would you rather spend time with? Which has options beyond "soar in and just flatten everything instantly"? If your only requirement for loving someone is that they always win, you might as well go the whole hog and be a Yankees fan.
Smugness and gunfire ... yep, it's New York.
But to hit the smug Superman even once, that's Batman's victory. To show what humanity can achieve with work and dedication. To face the impossible as a challenge and a duty. Superman is just swatting a fly. Batman is reaching out to touch the face of God. By punching it.
Luke also explains how the Dark Knight's Dumbest Moments Come from His Best Bat-Qualities. Everything he loves about human heroes is why Batman is his second favorite, and why he has 6 Objective Reasons Iron Man Is Better Than Batman. He also tumbles and responds to every single tweet. (He's especially interested in any other character-vs.-character battles you might have.)