Others with more experience will chime in.
But i would prefer a .22 over a .177 ONLY because accuracy is a little less of a concern. But you then need more fps with a larger caliber. With a .177 you need to be pretty accurate with larger varmint. The style of projectile makes a large difference too. Over penetration with a smaller caliber at higher fps is less successful in killing(i.e .177 at 1200 fps with a pointy nose pellet). Where a flat nosed pellet at low fps in .177, such as the "Destroyer", is more of a "punch" to a small rodent, much less a large ****. If I was buying a rifle I would buy a .22 with at least 1000fps, pretty good optics, and a hybrid round like the "Destroyer". This is all just my opinion, I may or may not be full of bull.
Cheers