Another advantage of using a separate binding is that the final sewing, if done by hand, is done on the back. From the front you see only a machine stitched seam, very even and strong. It is probably easier to make nice mitred corners when using separate binding. (I don't know how you make them when you fold the back over and hem it.)
I always make double-fold, or French fold binding, which is folded before being sewn to the quilt. I usually cut the binding strips across the WOF rather than on the bias, but bias binding does go around curves better and is supposed to wear better.