I have shot plenty with shotguns in .410 and 12gu, as well as a goodly number which felt the need to chew up my feeders with my .243 and my 25-06. Even with a head shot only there wasn't much left to haul in with me.
As of late however with the grandkids getting into the spirit, I have been working on them with my Bowtec Tomkat and my single cock air rifle. The bow is a hoot, but you have to really pick the shots as well as know about where your arrow will land. Even with the small game tips and judo type points they still fly a ways. I haven't gotten around to working up some with the huge fuzzy stuff on the ends just yet.
With either the bow or the pellet rifle heads shot drop them like a rock. It's a challenge though to get them to turn those heads when they are really snuggled up against the limb thinking they are hid.