I've never shot a squirrel before, but I would assume it's better to get them with a rifle than have to dig out the birdshot.
I came across an interesting anecdote in "The Lyon Campaign in Missouri : Being a History of the First Iowa Infantry". The author relates how the common way to shoot squirrels in Iowa before the war was by "barking" them. The hunter fired at the branch just below the squirrel's throat and the shock apparently killed it. This would preserve the meat. I suppose even if the squirrel didn't die it would be stunned and fall out of the tree, and could then be dispatched on the ground by smacking it against the trunk. At least that's how I'd do it.
Can anybody enlighten this city boy?