You don't specify, but if the scenario results from contradictory or paradoxical outcomes from either choice, you could call that a catch-22.
Derived from a 1960s novel of the same name, the canonical example of catch-22 is a scenario where a pilot that wants to fly more bombing missions in a war must be insane, and therefore should not be allowed to fly, but a pilot who says he is insane and should be excused demonstrates that he is rational, and therefore must fly the bombing mission.
I also like this quote from Nanny McPhee, which could be another example: When you need me but do not want me, then I must stay. When you want me but no longer need me, then I have to go. It's rather sad, really, but there it is.