This is not a difficult question. It's actually quite simple. We have very good scalable examples. Start with the ubiquitous .22lr and small varmints. You can shoot small varmints like chipmunks and gophers/squirrels. A 40 grain round nose lead bullet will kill them handily, but as a "bet your life on it" stopper that prevents them from crawling/running off it sucks. Sort of on the order of the big "stopping rifles", mostly works, but not always. But...Trade that 40 grain RN lead bullet for a 32 grain Hornet bullet and move it at somewhere north of 2000 FPS and it becomes a near perfect instant incapacitator. In my experience, it is effective on coon/woodchuck/porcupine/skunk size varmints, even if it no longer vaporizes them like it does with red squirrel and gopher size varmints.
Step up to a .243 or larger and shoot Mr porcupine with a tough bullet like a TSX?TTSX and it won't vaporize him or if it's not a vitals hit Mr porky can still waddle off, but back off the weight and use a lighter bullet and you're back to instant incapacitation with a body hit.
Step up again to 25-06 or .270 and start using frangible bullets at high velocity and while the vaporization in not so complete as the squirrel/gopher, it is still damned impressive on up to coyote size animals and can make a godawful mess of 150-200 lb deer as anyone who's shot deer with a 7mm RM or 300 WM with lighter, less sturdy bullets has learned.
You probably can't scale that up to the size and speed it would take to incapacitate a big bear or Cape Buffalo instantly and still fire it from your shoulder, but the body weight vs energy expended would likely be pretty linear. So, the stopping rifle tends to need someone with the skill to break the right parts to stop what the simple body hit cannot. You could certainly "stop" a leopard with certainty with a body hit with a bigger rifle and still fire it from the shoulder, but any toothy critter that's much bigger and I am going to put my money on the shooter instead of the weapon.
