Each gets 1 day of prep. Lets say they've never met and they think the others a villain in disguise. Morals on.
I think with morals on and random meet Batman Beyond could just say take this one, although I do remember an episode of Batman Beyond in which Bruce is bathed in the Lazarus Pit and becomes young again, and is vastly superior in his prime to Terry. That being said with batman's fighting skills and knowledge to adapt to a battle, he could take Terry as he takes flying and stronger opponents often.
This is close, good battle my friend!