Like a lot of these scenarios, it depends on how much time Batman would have to plan for it.

If they just picked him up and dropped him into a sealed cage with the xenomorph his odds of survival go down substantially.

If he's aware of the impending combat and manipulates the situation where he chooses when and where the combat takes place, the xenomorph's odds of survival go down substantially.

No prior knowledge of the fight in an area that gives no tactical advantage? Xenomorph

Prior knowledge allowing Batman to plan the fight ahead of time? Batman.