It's time for the Robot to lay down some knowledge. First off-
STOPPING POWER IS A MYTH. There is no such thing as "knock down" power. Especially not the literal knock down. Not even a .600 nitro will knock someone down, except maybe the person firing the gun. Shotguns don't knock people down either. The taylor knock out index isn't very useful because it lies in the domain of shooting very big animals with very big guns, and isn't germane to this discussion. The "velocity vs diameter" argument is also irrelevant because they are two sides of the stopping power coin, which I will argue is a fraudulent, counterfeit coin which was crafted by centuries of scientific misunderstanding of how weapons work. I won't even discuss hydrostatic shock because it's just such a hoax I don't even want to get going on it.
But again, stopping power is a myth. A .45 isn't going to kill someone in one shot every time. Shot placement is far, far more important. You can mag dump your trusty "stopping power" .45 into a man, but if you don't hit any vital organs, it is very possible for him to keep going. There are many incidents of people being shot an absurd amount of times and continuing to fight- and that's not just with "weak" calibers like the 9mm, that's also .45s and rifle calibers as well.
Here's a few interesting essays about the myth of stopping power:
http://www.supertrap.com/ST_Downloads_files/StoppingPowerMyth.pdf
This essay explains how "Stopping Power" proponents can cherry pick statistics to support their claims, when taking all data into account produces a far more nuanced picture of terminal ballistics. For a good summary of terminal ballistics and a lot of helpful charts, go here: http://www.frfrogspad.com/terminal.htm and here: http://www.rathcoombe.net/sci-tech/ballistics/myths.html
Here's another good essay:
http://www.firearmstactical.com/briefs3.htm
This really shoots down (Pun intended) the idea that because a bullet is larger and imparts more force on the object, it's more "powerful".
Consider the following:
Any handgun bullet you shoot into an attacker's body will deliver less energy than the energy transferred between the shoulder harness of a seat belt and the upper body of a 180 pound person during a head-on auto collision into a fixed object at 25 miles per hour. Consider the amount of "kinetic energy transfer" experienced by a NASCAR driver who survives uninjured, remains conscious and walks away from a spectacular collision at Daytona motor speedway, where speeds are almost eight times greater. A football pass receiver absorbs far more energy in his body, his internal organs subjected to much greater jarring shock, than any handgun bullet can deliver when he's running as fast as he can (15+ miles per hour) and makes a flying leap to catch a pass that's just out of his reach, and his body collides with the ground.
So basically, the actual foot pounds of force imparted by a bullet on its target is negligible in regards to the amount of damage that bullet does to its target. So basically you can't ever expect people to be killed by the sheer "power" of a bullet, because it's way within the tolerance range of the amount of punishment human bodies can take. The real damage done by bullets is the destruction of vital tissues and organs, a point that is illustrated elegantly by this next segment:
In November 1992, South Carolina Highway Patrolman Mark Coates shot an attacker four times in the torso with his 4 inch Smith & Wesson .357 Magnum revolver. His attacker, an obese advlt male who weighed almost 300 pounds, absorbed the hits and shortly thereafter returned fire with one shot from a single-action North American Arms .22 caliber mini-revolver. Coates was fatally wounded when the tiny bullet perforated his left upper arm and penetrated his chest through the armhole of his vest where the bullet cut a major artery. Coates, who was standing next to the passenger-side front fender of the assailant's car when he was hit by the fatal bullet, was very quickly incapacitated.
So is .22 the most powerful round? is .357 mag weak? No. But shot placement, or in this case random luck, is the most important factor in stopping an attacker.
That being said, there is some credence to the notion of stopping power though, but as this article states, it's Psychological. Many people have a concept of guns as "magic death hoses". You get hit, you're down. So actually, there are plenty of instances where upon being shot people collapse, despite no physiological reason to do so. Such an instance is also recorded in this article. But basically, this psychological response has little to do with the bullet's size, except if the victim has seen their attackers weapon and has prepared Psychologically to be stopped by "the big bullet". Bigger bullets may also cause more pain upon initial impact and a broader area of shock, contributing to Psychological component of stopping power. But that's IT. When it comes to "killing power" shot placement is what matters.
Another important factor in wound profiles and stopping ability is frangibility. Rounds that fragment within the body are more likely to hit and destroy vital structures like arteries, veins, nervous tissue, and organs like the heart, and therefore stop a target more reliably. So the terminal ballistics of a round can be quite important. A lot of times with handgun rounds though, you don't see so much fragmentation but often more of a mushroom expansion effect. So while a 9mm JHP is probably more efficient than .45ACP Ball ammo at causing lethal wounds, a .45 JHP is probably superior to the 9mm JHP in its terminal ballistics, because it will expand more.
HOWEVER- I'd also like to make the point that magazine size DOES matter. I think .46 ACP made a comment along the lines of "why shoot twice" or something to the effect. Aside from the fact that the idea of the "one shot kill/stop" is discredited, especially when it comes to handguns, I would argue that anything shooting once is worth shooting twice, even just to make sure. Additionally, hit rates in real firefights are extremely low. In the chaos of a firefight, your normal standards of accuracy go out the window. You may be able to get sub moa groupings at the range, but put yourself in a life or death situation and it will be a different story. The only way to train for such a situation is living it, and then there's the chance you won't survive your training, if you know what I mean. When that adrenaline is pumping through you, your accuracy and tactical competency go down. If you merely have your form and stance committed to muscle memory and can retain it during a firefight, then you are already have a huge leg up on most of the general public out there.
So where am I going with all this? Sacrificing hi capacity mags for a notion of "stopping power" can be foolish. You'll need those extra rounds, because a lot will miss and the ones that hit have a high probability of not doing their job. I've seen comparisons of 10mm auto to .40 S&W which has been lambasted as " Forty short and weak". 10mm is basically a more "powerful" .40 round. Check out this wound profile comparison for common handgun rounds:
http://img441.imageshack.us/i/orjdc5.jpg/
As you can see, the wound profiles for .40 and .45 are pretty similar, so the edge for .45 is pretty negligible. Therefore I would argue that 10mm Auto's higher capacity due to its capability to be compactly multi stacked make a far more enticing advantage than .45's "stopping power". 10mm auto, pound for pound, is probably just as capable a "man stopper", for whatever that is worth, as .45, and you much more easily carry more ammo. NOTE: Double stacked .45's do exist, but are much bulkier than 10mm.
So, now my huge rant is over, feel to pick at any mistakes or inconsistencies I may have presented.