I did forget to mention before, the ONLY disadvantage I really felt I experienced when shooting a "big bore" for small game like squirrels or rabbits is that every "bang" cost $1 a piece, while a .22lr or .22mag is more like a nickel or dime per shot. Granted, it's great to get the practice with your deer rifle, but doing it it very often adds up against the pocketbook.
These days, I have a custom Ruger 10/22 .22lr and custom built Bushmaster Varminter AR-15 .223 for small game, and I reserve my bigger bores for bigger game. Although I do have a .243 WSSM that I use for coyotes that I like popping cottontails with occasionally...