I've shot my share of critters with 177, 20 and some with 22. No doubt 177 with non-expanding pellets has less diameter and shock effect than larger and heavier 20 and 22. That said, with shot placement and good pellet choice, the 177 is very effective. I had the best overall results with dome pellets. In lighter powered airguns like a BSA Meteor (675 mv) and in a modified Daisy 790 (S&W 78/79G), the RWS Superpoint was a solid penetrator and killer.

The R9 in 20 with 14.3 Premiers was a winner with any solid hit. That said, I dropped tree squirrels at 70 yds with a FWB 124 with lung shots. The R9 did the same......

At close range a wadcutter is highly effective in shock effect but penetration suffers and downrange retained fps. I recall the original Benjamin pells were one of my fave in my BSA above that had a tad larger bore then German guns, being British....on the larger size for bore diameter.

Many factors, but in the end, any decent pellet thru vitals will take out common small game. Practice, learn your gear.