I'm assuming you've left out some crucial information - who belongs to which door. If you leave the doors out of it (they're inconsequential as you care about who each person is and the doors have no bearing on your decision making).

I happen to know the "traditional" response already - Ask either one if the other guy is a liar - only the liar will answer "yes", but I can't help having to point out a rather more obvious solution; just ask the fucking guy a trivial question and it'll be pretty obvious if he's the liar or not.

Now, that's obviously "too simple", but I can't figure out how to rephrase the riddle to take that solution off the table. It's almost like a riddle in itself.