Well, I can tell you that killing them with a bow is quite a bit more difficult. Last year, I went out 14 times with a bow. During those outings, I had a total of 15 birds that would have been high percentage shotgun kills - ie. bird is standing or walking inside of 40 yards and you have a clear shot at the head/neck area. Of those birds, I shot at 6 with the bow. Missed two, hit three, had one dodge the arrow at the last second. Two of them presumed fatally wounded got away. Finally anchored one on the last day. So if you want roast turkey, take the shotgun. If you want to have fun at the expense of a much greater challenge, use the bow.