If the writer likes Batman more: Batman wins.
If the writer likes Superman more: it's a tie or they're distracted and work together against a common third opponent. Superman fans are less awful.
If it's a fight to the death: neither of them kill people. Superman eventually wins by having a longer lifespan. Alternatively, Batman wins because Superman's died before and thus he outlived him.
If it's a race for who gets to the kitchen first: Superman, as he is much faster.
If it's a race for who gets to the kitchen first and Batman gets prep time: Batman builds the kitchen, starts in the kitchen, and wins.
If it's a race around the planet: Batman uses his superpower of money to hire The Flash, and wins.
If it's a competition of tragic origins: Batman's parents are dead, while Superman's planet is dead and in most versions so is his earth-dad. Superman wins, but since Batman is taking this worse, lets Batman think he wins.
If it's mortal combat and Batman has a kryptonite ring: Superman smothers him in lead at speeds faster than his eyes can follow.
If it's mortal combat and Batman has a kryptonite ring and infinite prep time: Superman likely also had such prep time and probably does okay with his laser eyes and ability to fight from space.
If it's mortal combat and Batman has a kryptonite ring and infinite prep time and Superman was screwing around for that infinity: the writer likes Batman.
If Batman has a really cool mech he suspiciously never uses for all the other cases it'd be useful: Superman probably rips it apart and leaves him alive.
If Batman needs to establish a mythos: Superman takes a dive in front of a cameraman.
If Superman needs to establish a mythos: he does something else impressive and lets Bruce abuse some children or whatever he does with his time.