Here's the epitome of that sense in carbines:
FN PS-90, 5.7x28. It's a small, fast round without much "stopping power," but it carries 50 of them in the magazine above the barrel. All in a gun that's 26" long and weighs 7.5 lbs fully loaded.
For every example of a person walking away from being shot with a 9mm wound, there's an example of someone walking away with a 10mm or 45 wound. The reality is that a shooting victim does not get blown over as shown on TV or the movies; bad guys, if motivated, keep coming until they are incapacitated (head/throat/thigh shots are good to stop that). Not motivated, even a graze to the arm will send them running. A man with a pulped heart can still actively engage for 15 seconds or more, whether that heart was pulped with a 9mm or a 45.
Stopping power really comes behind shot placement and capacity. Shoot your target to the ground - do not stop until they are on the ground. Whether that is 1 round or 10, you keep firing until they are down. That takes capacity, especially factoring in the misses that will inevitably happen.
Personally, I will take - and recommend - capacity any day. IMHO, better to have 100 rounds of a "weaker" caliber than 60 of a heavy caliber. And that is often the trade-off. A full-size 9mm frame pistol can hold up to 20 rounds; about the largest capacity you can get in 45 is the G21 at 13. Personally I will take the 50% greater capacity, knowing that I will miss at least half the shots I fire.
Conversely, there are plenty of stories about the adherents of the "spray and pray" school wasting an awful lot of lead and not hitting anything. One I heard from a local police officer was the two cops (I will suppress the name of their department just to cover their shame) who cornered a fleeing armed robber in an office park and emptied their Glocks AND all their spare magazines while the perp was emptying his little no-name auto pistol back at them. The only victim in the encounter was a dumpster about 75 feet off to one side of the conflict, it had a bullet hole in it. Otherwise everybody and their vehicles were completely unscathed. The perp apparently surrendered out of boredom.
Of course, your average cop thinks of his sidearm as just another tool like his nightstick or radio, and doesn't practice enough to sneeze at. But, still . . .
There are many more whitetails slain in the U.S. every year than people -- a much bigger sample -- and the fact that .223 is frowned upon tells you something right there.
Granted, marksmanship is always the key. That was sacrificed in military training for some years, but I understand it's making a comeback.
Here's the epitome of that sense in carbines:
FN PS-90, 5.7x28. It's a small, fast round without much "stopping power," but it carries 50 of them in the magazine above the barrel. All in a gun that's 26" long and weighs 7.5 lbs fully loaded.