We shoot a lot of Sporting and I reload nothing but reclaim, so I use a Mod choke in my 1100 Comp, as do my Gkids in their guns. Nothing succeeds like focus on the bird and the proper move to the target. We've taken a number of lessons from the Pro's, and the proper move is likely the most important aspect, far beyond shot size and choke. It's a rare occasion when I have to go tighter where we shoot.
On Rabbits, Andy Duffy and Jerry Meyers told us years ago - swing through! We haven't missed many bunnies since. It's all enjoyable, even more so when you hit more of them.