Well, the question is difficult and complex. Let us say, in theory, that Batman and Superman get into a fight. Batman, whose intelligence and with proper prep time, is considered to be great at anything. So as the fight gets in, he of course has his kryptonite in hand, cleverly hidden in his utility belt, with a batarang made of the kryptonite.
But don't count out Superman yet. Just as Batman is reaching for his kryptonite batarang, Superman, hoping to end this fight because Superman considers Bruce to be a friend, lightly taps Bruce Wayne right on the head. Of course, Superman's abilities make him underestimate the amount of strength he has, causing Batman to have a concussion. The serious brain damage Batman suffers from that leaves him in a vegetative state for the rest of his life. Superman, unable to deal with the guilt, (because both Superman and Batman are characters with moral complexities and not just bland number generating puppets who hit each other), spends the rest of his life depressed and sad.
He wonders, "Was there a way to save himself from hurting his friend in this way?" Then he looks up to the sky and angrily yells, "That wasn't me, that was you who did that! You're the one calling all the shots! You could have easily made him win, you could have easily done anything! I am one speck of dust on a cruel wind of fate! There is no free will truly for me, for any of us! You're the master of us! We live and die by your whim and your whim alone! Let me die! End this horrid punishment for me! Let me go from this mortal coil!" "What blood do you wish from me?" Superman would then say, weeping.
So in a fight between Superman and Batman, I give it to Superman.