I always chuckle when someone says 'predator hunting's because there are small predators up to large predators and the air rifle suitable for the bigger ones may be a bit overkill on the smaller.
I have a .357 Slayer, .357 Texan, .357 FLEX+ and a .357 Pitbull... Any capable and legal in Texas of taking a deer (or hog, coyote) but I'm not going to use one to shoot a (legal harvest) small feral animal or a raccoon, possum, fox, skunk, etc. light weight animal. For the smaller 'predator' at long range if 50 to 150 yards, I'm going to use my .257 Texan and it's preferred 85gr NSA BTHP. The various 40 to 65 FPE .25 pellet rifles I can grab out of the rack are used for short range or paid day/night neighborhood pest control, many times being those small predators listed above.