I just recently started machine stitching both sides (before, I machine stitched the front, and then hand stitched the back).
What I do: machine stitched front, then pull the binding around to the back and iron the heck out of it so that the fabric has "memory" and holds its position (the binding in the back is a little wider than what's in the front). Then use nice thick pins to hold the binding in place in the back and to prevent wrinkles. I then SID in the front to grab the binding in the back. It's virtually invisible on the front, and the back looks nice and tidy, if you iron and pin properly.