Over the years I have done most of my squirell hunting with a .22 LR & most rabbit hunting using beagles & a shotgun. Much of the territory in which I rabbit hunted swinging a .22 around after a darting rabbit at ground level would have been a most unsafe practise. I have sucessfully used ga's 28, 20, 16 & 12. I never owned a .410 & never felt the desire or great need for one. A light load of 4-6 shot through an open choke will not unduly mangle a rabbit unless shot "Underfoot". Most any game I killed I generally allowed to soak overnight in a brine solution which does much to remove blood & gut odors & tastes.
Rabbit hunting with hounds was the only hunting my dad ever really cared for. I enjoyed so many hunts with him. I would love nothing more right now than to go on another rabbit hunt with him. We never really tried to decimate the population, just got out, worked the dogs & picked up a few for the pot.