The cartridge is what you need to look at. The killing power will be defined by the cartridge not the gun.
The bigger ones are used for bigger game and longer distances. To shoot people, coyotes or deer you'd typically use one of the middle ones. To shoot squirrel one of the small ones, and elephants one of the big ones. To shoot something (e.g. people, deer) at 50 yards you might use something small. At a mile you'd need something big.
The "AR-15" (it's really an AR-style) shoot the same cartridges as other rifles. And typically they are the medium size cartridges. (That's the military definition. If they shoot bigger or smaller ones they are called something else.) One of the reasons to buy an AR-style is that, because of the modular design you can but a few parts and have one rifle that can be used to fire different cartridges. An AR-style shooting a .223 is almost identical to a so-called hunting rifle shooting a .223. The difference is not function; it's quality. A $1200 rifle is usually better than a $600 rifle - more accurate, lasts longer, less likely to fail. AR-style are typically better, but not necessarily. As I've argued, I don't know what the fuck AR-style means.