The stitch with the "zig" in it will hold up longer than the frayed edge will IMHO
I stitch right alongside the edge of the applique and then let the zig go over onto the applique piece. I like how it looks done this way and it protects the edges better, again JMHO :D:D:D
Here are some videos on applique, you may find them helpful
http://www.critterpat.com/content.php?content_id=1007