There's a few different mathematical methods people have created over the years that imbues some number scale rating of "knock-down power" or power factors to handgun cartridges. Looks nice on paper, and the math makes it seem sensible. It's just where the rubber meets the road in the real world where nifty knock-down and power factor calculations can start to fall short of expectations in making people stop in their actions.
People have also done calculations about the amount of "energy" capable of being delivered by trained boxers and karate practitioners, too, using fists and feet. A lot more "energy" can be delivered on-target by a skilled person punching or kicking than can be delivered by a bullet, but it's noticeably hard to knock someone off their feet unless they're either off-balance at the right moment, or something that holds them upright or helps them keep their balance is at least temporarily injured (skeletal/muscular or CNS/balance). Not the "sheer foot/pounds" of "knock-down power". It what that "power" may do, and does do, and where it does it (anatomically) that really matters when moments are ticking by.
Look at it this way, you can often knock a bowling pin off a table faster, further and with more "authority" by lobbing a softball at it, than hitting it with pistol bullet.
Of course, even 5.56 rounds barely knock over bowling pins at 50yds (we use that for informal and fun beat-the-clock/team competitions in some classes) ... but the rifle bullets can use their significantly greater velocity and bullet construction to usually cause significantly more wounding effect in soft mediums (and bony structures) than a low velocity pistol bullet.
Even the term "stopping power" is a bit disingenuous, or at least not consistently helpful, in choosing handgun calibers. The term "stopping power" is really more suited to being used when discussing brakes and motor vehicles.
Bullet design and construction (meaning good JHP design over ball/FMJ) and shooter controlled accurate shot placement are what really seem to count when all is said and done.
The nature of the wounding caused among critical tissues, organs and anatomical structures is going to play a critical role in how quickly some attacker may be "stopped", physiologically, from having the ability to continue making further volitional actions after being hit. Back in the earlier days of what became the modern study of wound ballistics and duty ammunition studies (late 80's), the FBI opined that an attacker falling down was "good". Not being "knocked down", but falling down.
Yeah, there's always the proponents of "hydro-static shock" (or otherwise described one way or another), too. That's another ball of wax, though.
All the different variations-on-a-theme contained within the wide spectrum of light/fast v. slow/heavy handgun calibers try to approach the "problem" (stopping attackers from doing bad things) from their own various directions, and sometimes they start to overlap one another in one way or another.
Perhaps not
totally correct. I've listened to another instructor working with the FBI (in a training capacity, and a very good friend of mine of some years) who has explained to me at great length that the experienced agents working as instructors, and a good number of experienced agents carrying the guns in the field (or, "doing the heavy lifting"), are firmly behind the switch to 9mm.
When you're talking about an agency that arms close to 10,000 people, though, you're going to hear all kinds of opinions from one day to the next. It's the reasoning and context behind the various opinions that makes it possible to occasionally start separating the wheat from the chaff, though.