Quandary-a state of bewilderment; a dilemma Dilemma- a choice between alternatives equally undesirable

They are very close and can be interchanged, but there is a slight difference in flavor. A quandary is a state where you are faced with a difficult situation and don't know what to do. A dilemma is a situation where you have two or more bad choices and have to choose one. In that case, it is not so much that you don't know what the choices are - you do know, but the choices are all bad.