Here in the uk power is restricted to below 12 fpe, .177 is the most popular calibre here, each years there must be hundreds and thousands of rabbits, pigeons, rats and squirrels that meet their maker courtesy of a .177 pellet.
Personally I prefer .20,in sub 12fpe it’s a little heavier and a little slower but the one I own is clinically accurate at normal hunting ranges (out to 65yards in perfect conditions) my highest tally on feral pigeons in one afternoon was 208 taken from the top of a grain silo, and in a few hours one night I cleared 108 rabbits from garden that had become over run with the little blighters.
so yes, sub 12fpe.177 is more than capable but shot placement is critical, head shots behind the eye below the ears is the sweet spot.
check out notts pest control uk on YouTube, he does good videos.
Bb