Just in reading here in the center-fire forums, the larger frontal area cartridges seem to hit an animal harder than a smaller one. I haven't bought an air rifle in a long time and I've have been perfectly satisfied with my old Sheridan .20 caliber pump up. Just extrapolating from using that, I've watched a crow fly a long way away before going down when I shot them with the pointy standard Sheridan pellet. I switched to the rounded front Beeman Crow Magnum pellets and the one crow that I shot with that pellet fell right over. I suspect that the .22 caliber pellets will be more available, but at higher velocity I might worry more about over penetration. On doves, chipmunks, rabbits or pigeons I don't think that you would see any difference, but on crows you might. I think that a .25 would hit them harder.
