I remember reading that binding on the straight of grain will fray sooner than binding cut on the bias, so I usually do bias on quilts I expect to be dragged around, like picnic, lap and baby quilts. Quilts that I think will be treated more gently, like bed quilts for adults, I have no problem using straight of grain for the binding. The only quilts I do a fold over from the back instead of a separate binding would be on wall hangings.