I use both, depending on my mood.
If it is a calm morning when the squirrels aren't as nervous and take a little more time feeding, i tend to use a 22, it ruins less meat, and no hard shot in the middle of a bite of squirrel pot pie :-)
If it is windy, or something and they are a little more nervous, I will use the scattergun.
As far as kinds of 22s and shotguns, I use either a regular Fieldmaster 22, or I have an old mossberg target rifle that has a big scope on it (heavy as hell but damned accurate)
As far as shotguns, If I am hunting in a wide open area of hardwoods, where i can see a decent distance, I will use a 12 guage with 3 inch magnums (for LOOOOOOONG shots) with size 6 shot, but usualy loads are regular 3 inch loads with 6 or 4 shot
For times when i am hunting in thicker stuff, I have a really old 16 guage I use with 6 shot, 2 3/4 inch loads.
Hope this helps!

Jennings Buckmaster Bow
.50 Cal Thompson Center Renegade