.380 is a difficult round to find good SD ammo for. It typically doesn't have enough power to both expand well and penetrate well. You typically have to choose one or the other- you can carry ammo that either penetrates well but doesn't expand or ammo that expands well but doesn't penetrate well.
Myself, I try to go by the FBI's standards for ammo performance- minimum of 12" of penetration through calibrated ordnance gel, maximum of 18", in both bare and clothed gel. The FBI also specifies expansion should be 1.5 times the original bullet diameter, but that really doesn't work for .380 because of the limited power available. The FBI protocols help ensure that the bullet can penetrate enough to reach vital organs from any angle while expanding as much as is practical in order to cause the most trauma.
In .380, there aren't many loads that can meet this standard. Most JHPs either don't expand and overpenetrate or expand very large and underpenetrate. Most FMJs massively overpenetrate since they don't expand at all and are virtually guaranteed to overpenetrate. Also, because of the extremely elastic nature of most human tissues, FMJ wounds typically aren't large at all because of the skin and tissues snapping back into place after the bullet passes through them. Hitting critical areas with FMJ can work, but the person can take a LONG time to bleed out if you miss things like the heart, brain or spinal cord. JHP ammo works better for this because they damage more tissues and can help with the target bleeding out and loosing consciousness.
Luckily, we live in a time when gel testing is fairly widespread and available on the Internet. There are quite a few people doing testing and publishing their results. One of my favorites is Shootingthebull410 on Youtube. He is very meticulous in his testing, properly calibrates his gel blocks and uses the same denim material that is used by the FBI for testing. If you go this route, just be careful and educate yourself to make sure that the tester is using verified testing techniques. With watching his testing, along with a few others, I have come to a few conclusions.
The best performing .380 JHP ammo seems to be any of the various loadings using Hornady's XTP bullets. The XTP expands, but does so modestly, meaning that it still has energy to penetrate well. XTP reliably penetrates over 12" and also reliably expands, but expands to small diameters. There are some other loads that gain honorable mention, such as Speer Gold Dots. They don't reliably penetrate to 12" but do reliably penetrate to 10-11" and expand well. That's the toss up with .380. You can have good expansion or good penetration, but not both due to the lack of energy in the cartridge. Also, check any resources you come across and see what gun or barrel length they are using. Lots of times, manufacturers use longer barrel lengths than what are typically found on carry guns to make the numbers look better. That's one thing I like about Shootingthebull 410, he actually uses a Taurus TCP in .380 with a 2andsomething" barrel, which is equal to most of the sub-compact .380s like the LCP. This gives you more realistic results than, say, Winchester using a 4" test barrel.
About all you can do is do your research, decide what you want for performance and pick a load that matches your performance goals. You can have penetration if you want it or expansion if you want that. It's all up to what you want the gun to do. Myself, the PD I work for is currently using Speer Gold Dots for .380. Since I am the head firearms instructor and am in charge of buying ammo, when we run out of Gold Dots, we will be using Hornady American Gunner, which uses the XTP bullet.
Bub
