Assume a pellet is just scaled up from .177 to .22
Mass is proportional to cal^3
Drag is proportional to frontal area * velocity ^2
Frontal area is proportional to cal^2
Velocity for a 12ftlb rifle is proportional to cal ^-3/2
So Drag is proportional to cal^2 * (cal^-3/2)^2
Or Drag is proportional to 1/cal
Energy lost is Drag * distance travelled
So the .177 loses energy 24% faster than a .22 initially.

BB