A few thoughts...
1) all handgun calibers are under powered when it comes to stopping an assailant.
2) Bullet placement is paramount as "stops" come in two flavors:
- the half that are "OMG I've been shot! I'm going to stop doing what ever got me shot!" type of psychological stops; and
- the other half where you need to hit the assailant in the central nervous system or in the cardio pulmonary system to get rapid incapacitation. One shuts off the nerve impulses and the other drops the blood pressure quickly (still 10-15 seconds).
If you don't get a psychological stop, you need good bullet placement.
You are also going to shoot and then keep shooting until the assailant is down, regardless of the caliber you are using.
3) People will argue for ever regarding the caliber requirements.
The FBI wants expansion of at least 1.5x original diameter and 12-18" of penetration (and that last 4" is arguably more than is needed). The benefit of this kind of ballistic gelatin data based approach is consistency in rating and comparing various calibers and loads.
The downside is that the gelatin data and the performance minimums were derived based on an imperfect theoretical model, and that model doesn't always explain actual results on the street. Ideally you should be using the real world results to inform and revise the results of the model.
For example, if you are carrying a .380 ACP, you need one of a half dozen loads, all using the 90 gr Hornady XTP at around 1000 fps to meet the FBI minimum. However, there are other loads that have performed well on the street.
4) barrel length matters a lot in the .380 ACP and the .38 Special.
A good .380 ACP load in a 3.5" -3.9" semi-auto is more effective than a standard pressure .38 Special out of a 2" snub nose revolver, and the best .380 ACP loads are as good as many .38+p loads in a snub nose revolver. And most .380 ACPs offer 7-8 rounds compared to 5 or 6 for a J or K frame revolver.
5) what ever you carry you need to be able to shoot it well under extreme stress and the vast majority of people who carry a handgun for self protection (including police officers) are not as skilled as they should be.
In an actual self defense situation you will devolve to your lowest level of fully mastered training. For many that operationalizes as pointing the gun in the general direction of the bad guy and pulling the trigger.
6) Carry the largest, most effective caliber that you can shoot accurately under practical combat conditions.
For most folks a 9mm Luger is a good middle of the road choice and it balances speed, power and magazine capacity pretty well. If you are a revolver, guy a .38 +P is probably the choice, unless you're carrying a K or L frame and are well practiced and skilled with .357 Mag.