Having shot lots of game from Elk down to gophers, with pistols, shotguns and ARs, the AR is the most effective and the pistol well behind. Sure, with high velocity slugs and buckshot, the shotgun is equal to or superior to the AR in terms of energy on target, but a scant few use those premium type high velocity rounds of SD.
The component that always strikes me when I am at the range with students who are smaller, weaker, disabled, etc. is that I have yet to find a person from 6 to 90, missing fingers, hands, legs, vision issues etc that can not, with relatively little effort, be taught to shoot the AR platform quickly and accurately. The same can not be said for the handgun or shotgun.