I used Broadheads for pheasant this past winter and think the small snaro might work better at knocking down the bird, unless it is a head shot or centers the chest cavity probably won't kill it right away. Pretty hard to center a small pheasant with a broadhead for a quick kill when it's not moving much less when it is flying.I also know some dog owners get real nervous about broadheads which I can understand.
On a smaller bird I would definitely use a bigger head like a snaro. I think any small game head would work for all the birds, but your margin for erro goes way down from a big head like a snaro...3rivers has them in 2, 3 or 6" The 2" looks interesting for something pheasant sized, but haven't tried it yet.