Jim, I have to respectfully disagree. I see your point, but I contend that there is a "stopping power" capability out of handguns. It comes in the form of the bullet being capable of producing such overwhelming neurological and physical trauma that body parts simply cease responding to inputs, rendering a threat null.
Apart from a hit to the central nervous system's "control center" (i.e. the base of the brain or the upper spinal cord), handgun bullets simply don't have enough power to accomplish that, at least not instantaneously.
After a hit to the central nervous system, the next quickest route to physiological incapacitation is circulatory collapse. To achieve this, you need to hit the heart, a major blood vessel, or a major blood bearing organ (e.g. the liver). Unlike a hit to the central nervous system, this is not instantaneous. It can take from seconds to hours, depending on what the bullet hits. There is sufficient oxygenated blood in the brain and the muscles to support full, voluntary action for
10-15 seconds after the heart has been destroyed. This is an eternity in a fight.
Of course, that doesn't mean that everyone who gets shot will keep fighting as long as he is physically capable of doing so. Actual gunfights show that physiological factors may actually play a relatively minor role in achieving rapid incapacitation. Usually, psychological factors cause incapacitation first. In other words: the assailant basically gives up, even when his body is actually capable of carrying on. Unfortunately, there is no way to predict whether the guy you shoot is going to be a coward who gives up upon being wounded, or a mad dog killer type (like the two bad guys in the Miami Dade shootout) who will fight until the last second when his body fails. Nevertheless... Barring a central nervous system hit, there is
no physiological reason for an individual to be instantly incapacitated by even a fatal wound. If he's one of the mad killer types, he can keep going until blood loss is sufficient to drop blood pressure and/or the brain is deprived of oxygen. Trauma alone won't make much difference. In a fight pain is commonly suppressed in the aftermath of serious injury such as a gunshot wound. And even if it isn't, it has to cause an emotional response. Actual incidents show that in many cases, pain is either ignored or else motivates the subject to anger and increased resistance, not surrender.
In short: handguns have little to no "stopping power," speaking purely of physiological effects.