In my experience they do with heavy shot loads. With light shot I've never noticed much of a difference. I have both standard bore 12 gauges and back bored 12 gauges. With a heavy turkey load of 3" #5, I get a more consistent patterns with my Winchester SX4 with its Invector + than I do with my Ithaca M37. The difference isn't huge but it is noticable. They're supposed to pattern steel shot better, too, but I don't waterfowl hunt so I don't know about that.

If you ever want to shoot a rifled slug out of a smoothbore, you'll need a standard bore. It doesn't work so well out of a backbored barrel.