I'm a little surprised no one has brought up hydrostatic shock yet. This would probably be the time since we've explored the less controversial and more scientifically verifiable aspects of the cartridge. If you're not aware of the theory of hydrostatic shock, it's basically a fancy term for stopping power, or more eloquently put, the purported ability of a bullet to remotely damage the nervous system and blood vessels via its shock wave. Under this theory, it is indeed possible to incapacitate and even kill someone without hitting a vital organ directly.
Army researchers in WWII confirmed the phenomenon, researchers in Vietnam questioned it, and studies out of Iraq then reconfirmed it, noting that remote wounding was significant in all cases of rifle wounds at close range.
Here's the thing: the researchers who believe in it say that remote wounding effects are measured as significant (i.e. capable of producing life threatening injuries to the nervous system and organs) at around 500 ft/lbs of energy. As we all know, .38 Special falls in around 200-250 ft/lbs, whereas duty calibers fall right at around 500 ft/lbs or more on average. Thus, there may in fact be a tangible reason to choose 9mm, .45, .40, etc. over .38 Special.
I would be interested to know how many people here believe in hydrostatic shock, and out of those how many believe it's a significant factor in stopping threats with standard pistol caliber cartridges. I myself do believe in it, but do not believe it's a big part of the equation in "stopping power" until you get to rifle calibers, or magnum pistol calibers at the very least. I've just seen too many videos of people being drilled repeatedly with everything from 9mm to .45 and seeming to be unaffected by it. Were hydrostatic shock a big part of the equation for pistol calibers, I would have to think that five rounds of 9mm to the chest would produce the desired result. I've come to believe that 99% of the time the only way to stop someone using a pistol is to hit them in the heart or the head, or in a large enough blood vessel that the sudden drop in blood pressure will cause them to lose consciousness, at least momentarily.
I would be interested to hear everyone's thoughts.