Selecting carry ammo (based on 20+ years as LE firearms instructor):
1. Ammo has to function reliably in the pistol, as tested by the CCW holder. It has to be tested in the weapon by the shooter. Eg. Ball usually works reliably, but not always… I had one brand that was not reliable in a particular gun. Every specimen is different, every shooter different. You must test it.
2. Ammo has to be shootable by the CCW holder in the weapon. Accuracy take precedence over some marginal factor of "power". Eg. I like the Speer 90 grain GDHP, but in the LCP and P3AT the recoil is uncomfortable and accuracy suffers. Much better in the SIG P238 and S&W BG380.
3. JHP ammo in .380 is designed to expand at the velocities of small pistols and will create somewhat more damage than FMJ ammo. However, JHP will penetrate less than FMJ… how much less depends on the particular design. For close-range frontal attacker (usual scenario), JHP .380 from the major manufacturers penetrates enough on someone wearing light clothing: 9-13" generally. That is sufficient for most close-in self-defense that you would use a .380 pistol for (as opposed to LE work where you are actively pursuing dangerous armed and aggressive criminals). However, put some heavy winter clothing on the attacker and that JHP penetration could become <9", which is not a good thing.
4. In .380 only, I carry JHP spring-fall, and FMJ in the winter. I live in the Northeast. If I lived in Miami Beach, I'd use JHP all the time. In the LCP/P3AT, I use standard Federal 90 grain JHP: it is accurate, recoil is moderate, expands to some degree, completely reliable, and not priced like gold. In P238/BG380, I use Speer 90 grain GDHP… it's accurate and reliable but has more recoil than the other rounds, also expands more. There are other effective JHP out there as well; my choices are not exclusive. For FMJ ammo I use 95 grain Federal American Eagle. The Winchester flat points seem like a good idea but in gel testing they don't have any different effect than regular FMJ, and would not be as reliable as round nose FMJ.
5. Overpenetration as a hazard is largely a myth. The majority of rounds fired in shooting situations completely miss the intended target, and go downrange at full velocity. Are you worried about those rounds? If not, do you always shoot with 100% accuracy? If you are worried about a round that expends most of its energy and velocity in a human body prior to exiting, and then with very slight probability strikes someone directly behind the target, perhaps you shouldn't be shooting at all in the particular situation. However, if your round fails to penetrate adequately, and no vital organs or blood vessels are struck, your attacker will not be incapacitated, and you will more likely be killed or severely injured as a result. I'd rather have enough penetration, and be aware of what is behind my target.
6. IMHO, don't waste your time and money on things such as Buffalo Bore. You are paying an exorbitant premium for ammo which for the most part is loaded to a non-standard and/or potentially unsafe level, and which is not been shown to be any more effective than standard ammo… marketing claims to the contrary. They have some good loads not otherwise available, but not better enough to justify the price. On top of which, shooting enough of the Buffalo Bore to ensure than it is reliable and you are accurate with it, is damaging to both your weapon and your wallet. Eg. Difficult to find a better .44 Special load for the Charter Bulldog than Federal 200 grain LSWCHP.