I do apologize if I'm re-hashing previous points, as i reached the TL;DR point about the end of page 2, but wanted to drop my .02...
1. All common pistol rounds suck for stopping a fight. None of them consistently exceed the "rule of thumb" 1800fps that is (or was, if I'm out of date) considered to be the bare minimum to cause "hydraulic shock," defined as the energy transfer being enough to cause shearing damage to tissue beyond the permanent wound cavity, as most rifle bullets will do. That said, pistols are easier to carry, easier to conceal, and are therefore much more likely to be available to you if you have to face an assailant as a civilian, and they're definitely better than being unarmed, or armed with only a knife or similar non-ranged weapon.
2. Since pistol bullets don't induce hydraulic shock, that means they only damage tissue that they actually pass through, i.e. the permanent wound cavity. Expanding bullets make the frontal area of the bullet larger, which means incrementally increasing the odds of hitting something vital as it passes through tissue. Good expanding bullets increase the diameter of the projectile by 50-100%. They also slow the bullet down more as they pass through the body, meaning any round that exits is less likely to strike someone other than the target with potentially lethal energy.
3. The bullet has to be able to consistently penetrate to hit vital organs if it is to have a chance of stopping an assailant. It may have to pass through an outstreched arm, or through the body at an oblique angle. The FBI studied a LOT of actual gunfights involving both police and civilians, and came to the conclusion that ideally, a round should penetrate 12-18" in calibrated 10% ballistics gelatin to ensure adequate penetration.
4. Train to be able to score consistent hits to the center of mass rapidly and repeatedly. Accurate is better than fast, but with practice, speed will come on it's own. Remember the old saying, "you can't miss fast enough to win." Practice until you can draw and fire consistently into a 4-6" circle between 7-10yds as a minimum, IMO. Also remember, your marksmanship will likely deteriorate by half or more under adrenaline and fear for your life. Your sight picture and trigger pull should be instinctive, because you likely won't have time to think about them if you need them. Don't just practice double taps, either. Practice firing from singles to whole mags. If your life is ever on the line, you will need to fire until the threat stops.
The link to the Luckygunner test series is really handy for finding ammo. Their test is consistent across all calibers and rounds, and while their gel isn't EXACTLY the same as the FBI's organic 10% gel standard, it is similar enough to give a good, consistent comparison across the board. I recommend trying to find a round that expands as big as possible while still falling within that 12-18" average penetration range. Pick a couple options, hit the stores or the internet and try to getsamples of each. Test fire them to see which gets closest to your point of aim while feeding reliably. Different weights and loads may produce vastly different groups and point of impact. For example, my wife's Sig .40 shoots 3-4" low at 10yds with most 165's but to point of aim with 180's.
And some examples from me:
Winchester .45 ACP 230 Ranger-T +P
Remington Golden Saber 185 +P
Same gun, same day, 10rds at 10yds. Obviously the Winchester is the better choice for my particular application.
