I chose .45 ACP
Mostly because I'm a loyalist.
Stopping power is a much used and much misunderstood term. I much prefer the term 'immediate incapacitation' because it comes with a definition. "Immediate incapacitation is defined as the sudden (2) physical or mental inability to pose any further risk or injury to others." (From PART 1 OF THE FBI PAPER ON HANDGUN WOUNDING FACTORS AND EFFECTIVENESS, July 14, 1989,)
http://www.pointshooting.com/fbipart1.htm
In a self defense setting (which includes most of law enforcement encounters) one uses a firearm against an attacker to prevent that attacker from carrying out or finishing the attack.
Just what causes this is still under discussion. Grab a beer and a stump and sit down, this will be a while. The actual effect is argued, some say it cannot and does not happen. Others claim it does, but don't have proof of what causes it, unfailingly. Frankly, I think there are enough reports of people being shot and instantly 'freezing up' to believe it does happen. Nor, from the reports I have read and people I have interviewed, do I believe is it merely a psychological effect.
There are a couple of widely agreed upon factors.
One is bullet placement. The shootee has to be struck in the Central Nervous System or near to it. It must be noted a 'heart shot' will kill a person, but does not guarantee an immediate cessation of hostile actions.
The second widely agreed upon factor is energy transfer. Somehow the bullet must transfer the energy contained therein to the villainous individual that has driven us to the extreme measure of shooting him. (Or her, I don't want to be sexist here.) Not agreed to is the manner of such transfer. Some require a bullet to alter shape (expand) and use up all energy in stopping within the body of the target. Others believe a flat fronted, sharp edged bullet shape tears and distorts enough body mass to transfer energy. A third belief is that of dwell time, wherein the bullet moves so slowly it transfers energy to the target while transversing. (This last was the belief of the British War Department; their .380-200 revolver - a .38 S&W case launching a 200 grain RNL bullet at about 700 fps - gave stopping power much higher than presumed from the figures.)
Another widely agreed factor is sufficient power. The bullet delivered has to have a certain amount of 'oomphf' or 'horsepower'. What is not agreed to is
what constitutes this sufficient power. Some folks posit kinetic energy as the secret weapon and some think momentum is the magic spell. (Just to save any guessing, I'm a momentum proponent.)
As I said, the argument lingers on. And on. And on.
I like big cross sectioned heavy bullets with flat fronts and sharp shoulders and a strong velocity.
The fact is, both .45 ACP and .40 S&W with decent loadings are pretty good defensive rounds. Now what the shooter does with them is another story.