When I was young, we would hunt both rabbits and grouse with a .177 caliber air rifle and found them fine for hunting.
We made it a point of using pointed pellets while hunting:
A selection of .22 pointed pellets: RWS Superpoint, Beeman Silver Sting, Beeman Silver Arrow and ARS Cobra.
The head of a pointed pellet is just that. It ends in a very sharp point that provides maximum penetration on small game. Pointed pellets were designed specifically for hunting and field use. The waist area of pointed pellets is larger in diameter for increased weight without unbalancing the front-to-rear weight distribution, which would destroy accuracy. The skirt area is shorter than a wadcutter skirt. Some pointed designs feature forward-driving bands. These are flat bands around the head, in front of the waist, that increase the surface area that engages the rifling. Increased rifling engagement area provides better accuracy and longer range, but also increases pellet-to-bore friction that must be overcome--or velocity will suffer. For this reason, pellets with forward-driving bands work best in magnum air rifles. If you want a standard-velocity rifle or air pistol for hunting, choose a pointed pellet without forward-driving bands--or one of the hollowpoint designs...
The pointed pellet really is the best choice for hunting. I’ve spoken to many airgun hunters who rely on pointed pellets for humane, one-shot kills on small game. Their other advantage is that they're very accurate. In fact, I've shot some air rifles that grouped pointed pellets better than they did wadcutters. But they do cost more, and their pointed design is very destructive on indoor targets. So, for informal plinking and target work, the wadcutter is still your best bet; but if you're in the field and looking for game, the pointed pellet can't be beat. - The right pellet makes a difference