Duh. Dr. Who. He could travel back in time to when Bruce Wayne was a child and shoot him along with his parents.
I'll bite. Doctor Who would win. If he lost he'd just go back to Batman's childhood and kill him. Of course he's so clumsy he'd probably miss and wind up killing someone close to Bruce instead thereby turning him into the Batman...omg
It is clear in the Dr.Who universe that Dr.Who does not kill. He hates guns. So no, he would not go back in time and shoot batman but instead prob save batman's parents and that would stop "Batman" from ever existing. Rookies...
Back to the kitchen to make RKReborn a sammich? J/K Doctor Who would win. Batman is the perfect human being, but Doctor Who is better than human.
So is Superman and Batman's made a meal of him before. When Batman is matched up with super-powered beings, he typically wins. I expect the message of him always winning out has something to do with the specific dichotomy you cited. In other words, there is no such thing as "better than human" or whatever.
This is a completely hypothetical situation. In the "real" world/universe, batman and dr. who would have no business fighting each other. so one may toss out certain morals the original character may have retained in their shows. based on pure ability, dr. who trumps batman. The ability to time travel >>>> anything batman can do. the whole charm of batman as a character is that he does not possess any supernatural powers.