As I understand it, MathStackExchange is for homework level questions and MathOverflow is for research level questions. As a student, I always posted in MathStackExchange unless I had some weird question that came up in undergraduate research.
However, as a beginning graduate student, I'm starting to ask for facts that might not be contained in a basic textbook, but are still very basic for experts in the field. When I ask on MathStackExchange, it gets read by very few people, not because the question is hard, but because it is specialized for the audience. (In addition to the two or three on my main account, I have a couple more on a separate one.)
However, I'm afraid (and know for some of the questions) that asking these on MathOverflow would probably not go over well. Do you know how to tell when a question that is not research but is better answered by an expert is appropriate for MathOverflow?