After studying the matter for over 30 years and consulting with engineers in the industry in my capacity as a firearms writer and after talking with police and a physician who studied wound ballistics before advising Dallas PD to adopt lead HP .38 ammo to replace their old RN bullets, I've settled on Federal HST or Speer's Gold Dot. Some others also work so well that they are probably as good, at least most of the time.
Sorry for that first run-on sentence, but I want to make clear that I didn't just read posts on the Internet to reach my conclusions.
The reason why I chose these is largely that they expand well and penetrate well and are unlikely to shed the lead core. They penetrate a variety of mediums like glass and denim about as well as anything short of a FMJ. In fact, in some applications, I'd use a FMJ, but not for typical home defense, which is the issue in this thread.
FMJ is largely denigrated because it won't expand. But the person whom I know who has shot more people than anyone else using a handgun (15; nine with a 9mm and six with a .45) used GI ammo quite successfully, largely because he can shoot very well indeed. But he did have to fire more than once if the bullet wasn't immediately effective. He found the .45 a little more potent, but not vastly so. He prefers the .45, but ammo was harder to obtain in Iraq, and spare magazines were at a premium. Now in private life, he has both 9mms and .45s, generally carrying a Colt Govt. Model which he has tuned slightly. His ammo of preference in both calibers is HST. But that was denied him in military service, due to the Hague Accords. (Not the Geneva Convention, as some think.)
He never hit anyone with either caliber who didn't drop, but in a few cases, finishing shots were needed. He was unable in a few cases to determine for sure that the enemy died, as he was on the move, under fire. (He has been wounded three times.)
Additionally, I was acquainted with the late David W. Arnold. Some of you will recall him as an editor of Petersen's Handguns. Before moving to the USA, David was a senior police official in then-Rhodesia. (He was born in South Africa, doing his national service there as part of a tank crew.)
He had access to after-action reports from both soldiers and anti-terrorist police units. The ammo used was normally FMJ military style. The 9mm fared pretty well, whether from pistols or SMG's. He didn't feel too unarmed while carrying his issued P-38, although his real preference was for a Colt .45 auto. I have no way of knowing how well placed those bullets were, and I'm sure that the average soldier or cop there wasn't a world class marksman, like David. (He shot on the Rhodesian national IPSC team.)
If it interests anyone, my home defense handguns are either .38 or .357 revolvers, using Plus P .38 Gold Dot or Hydra-Shok ammo, or a 9mm Beretta M-92FS with 124 grain HST. Snubs or three-inch barrels get Speer's Short Barrel 135 grain load.
I also have some lead HP 158 grain ammo from Federal and Remington. Dallas police experience with that basic load (they issued Winchester at least some of the time) was positive. One officer killed six suspects with it, using his issued S&W M-64. They also provided Winchester Silvertip 145 grain JHP .357 ammo for those wanting to use a .357. The only comment that I've been able to get about the .357 load is that it was "extremely effective."
I do believe that some bullets work better than others, but agree that placement is the single greatest factor in stopping power.
Oh: in event of a likely riot or looters, I'd load my 12 gauge and maybe a .303 which has a 10-shot magazine. The load for the .303 is Winchester 180 grain Power Point hunting ammo. I will be quite surprised if either doesn't stop an enemy with one shot, let alone two. I could use a 'scope sighted hunting rifle in other calibers, but proving self defense might be difficult if I had to shoot anyone too far away. It's not out of the question, if he was delivering accurate fire toward me, but is an unlikely situation. (If there is a total breakdown in social order, long range capability is more likely to be needed.)
Oh: I just remembered reading the late Che Guevara's book on guerilla warfare, of which he had extensive experience. He recommended the .45 for pistols, as it worked better than 9mm from a handgun. I think he said that the 9mm was okay in SMG's. But I read that book in high school, which was a long time ago.