over the past two years or so i've killed a stack of squirrels with a couple of beeman break barrel springers. i started out with a beeman R7, which is their smallest, lightest rifle. i decided that the R7 is too light unless you are willing to get really close to the squirrel and wait for a perfect head shot. it was murderous on starlings in the backyard, though.
next i got an R1, which is beeman's original "magnum" air rifle. it hits with a lot more authority. most of the squirrels i have killed have been with this one. it will send a pellet all the way through a squirrel at 30 yds. you still have to be very careful with shot placement, though, much more so than with a .22 lr.
my problem with the R1 is that i don't shoot it as accurately as the R7. it has quite a bit of recoil, which makes my groups sometimes inconsistent. also, it periodically loosens the screws on the scope i have mounted on it, loctite notwithstanding. its also a big heavy rifle, kind of a PIA to carry anywhere.
so then i got the HW50s, which is midway between the R7 and R1. i shoot it much more accurately than the R1, and it definitely hits harder than the R7. doesn't loosen scope screws. i have killed several squirrels with it, but i've also had a couple get away or require a finishing shot.
bottom line? doesn't matter which one i use, the rules are the same: i have to get real close to get consistent, repeatable kills with an air rifle. the hw50s and r7 need to be close so the pellet will have enough energy to kill, the R1 needs to be close so the groups will be small enough to be precise. i will say that the HW50s is my favorite, because it is more powerful than the R7, and more accurate (in my hands, at least) than the R1.
all of them take more skill and patience to use for squirrel hunting than an ordinary .22 lr rifle. but i guess that's part of the fun. if you pop over to one of the airgun forums, you will find some dudes that have airgun hunting for squirrels down to a science.