The question I have is how many acres are you trying to defend here?
I have a Gamo single pump air rifle and it's taken out a number of rabbits and muskrats without a problem. I suppose the range is sub 80-90 ft. Anything more than that and I tend to grab the old Ruger 10/22.
Nonetheless, if you are shooting at vermin in your front yard at relatively short ranges, I'd go with the air rifle. The upper crust models are amazing nowadays compared to the old 760s I shot as a kid. With a muzzle velocity approaching 1200 ft/s, it's like a one pellet shotgun. Only drawback to them is reloading time. A single shot break action isn't very forgiving when you miss and need to do a quick follow-up shot. That's where the 22 LR is nice, in whatever model you choose. The 17s are also pretty nice, but ammo is quite a bit pricier even if it isn't prohibitively expensive.
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note: my Gamo has a similar recoil and nearly as much bark as a 22. I was shocked when I first shot it.