Combatants :

Batman (Kirk Langstrom)Justice League: Gods and Monsters	vs	Batman (Bruce Wayne)Justice League: The New 52
Characteristics: Vampire level strength and speed. Enhanced agility and reflexes. Self sustained flight. High resistance to injury		Characteristics: Peak human strength and speed. Agility and reflexes honed by years of training. Batclaw and cape glider. Standard Batsuit protection
Standard canonical personalized equipment.		Standard canonical personalized gear.
Resources comprised of stolen medium and high tech components.		Resources available in the Batcave.

Background:

An accident pulls Kirk Langstrom from the Gods and Monsters Universe into the New 52 universe. He sets up shop in Gotham city while he figures out a way back. That night, while searching for a suitable meal, he comes across the Joker and Harley Quinn and a whole bunch of their hostages. He slaughters the henchmen and drinks the Joker and Harley Quinn dry before freeing the hostages. The hostages report that they were saved by a 'Vampire Batman'. Word gets back to Bruce Wayne and he becomes determined to catch the murderous 'impostor' and clear his name. Meanwhile Langstrom finds out about this 'other Batman' and realizes that it is only a matter of time before he comes for him. Both of them seek to learn more about the other, in preparation for the inevitable clash; Langstrom, from the public records and the criminals that he interrogates before killing them; Wayne, from studying the dead bodies and questioning eyewitnesses. After a cat and mouse game over several nights, both of them unexpectedly come face to face over a random section of Gotham that they're both familiar with but neither has had time to prepare.

Rules:

One on one combat, on rooftops or indoors, using whatever weapons and equipment that they may carry on their person. (No infinite utility belt and no Insider suit. That was just bad writing imo.) The standard medium Batsuit is allowed. Langstrom is limited to the suit he had on him when he came through. No resupply or backup for either of them. Victory by death, KO or immobilization.

Scenario 1: Morals on for both

Scenario 2: Langstrom is bloodlusted but sane and Batman has no problem killing a vampire

Who wins?

I'd put my two cents on Langstrom, but I'd be interested to see what others think.

Difficult decision but Batman would have collected enough data on Langstrom and Langstrom would be beaten by The Caped Crusader

Batman

Batman+Prep doesn't necessarily mean an automatic win. The only information source Batman has to go on are the dead bodies and there isn't any info he can glean from them that would point to a definite weakness. Ultimately what this battle comes down is Wayne's human level physical skills backed by the Batsuit (it is a crucial tool to balance the fight; he'd be stomped without it), and Langstrom's greatly enhanced natural skills. Langstrom presumably has his own equipment, though probably not on the scale that Wayne does.

Could go either way, but I still think Langstrom.

First of all Batman (Bruce Wayne) has fought vampires before, specifically Dracula, and gotten his ass kicked in one on one combat. Kirk is much faster and stronger and may not have the better technique but will easily kill Bruce, in the conditions stated above, especially since Bruce would have very little previous knowledge on Kirk and Bruce's primary strength in a fight is his understanding of his opponent's powers, weaknesses, and strategies. If the circumstances were less constricted Batman (Bruce Wayne) would lose the fight but would probably escape and thus research his opponent and be ready for the next fight. Overall in most scenarios, Kirk would win but with time Bruce could gain an understanding of Kirk's abilities and devise a plan to defeat him. Plus in a fight to the death, Batman's (Bruce Wayne) morals would restrict him from killing Kirk and Kirk doesn't have such restrictions.

Batman rofl stomps this imposter.