Around my house, I use my .117 spring piston pellet gun. Its plenty powerful enough to drop a rabbit at the ranges I can get close to them at. Yeah a .22 may be able to drop them from farther ranges, but I guarantee if you shot a .22 at the ranges I get the rabbits at, they would take off before you could blink an eye. With a pellet gun, they just sit there like "wtf was that?"

But for squirrel I use either a .22LR or a 20ga 6 shot.