The above advice is the conventional wisdom, but it's a bit dated now and really leaves you at a disadvantage with an already marginal caliber. .380 FMJs make pitifully small holes and while penetration is important, the FBI standard stresses both 12-18" penetration as well as expansion to 1.5 times the starting diameter. If it were a case where no .380 FMJ round could make the minimum penetration then I'd agree that FMJs are the way to go - but that's just not the case with the Hornady 90 gr XTP being available.
The you tube link in one of the previous posts is pretty much on the mark, but you need to consider that he's talking about a short barreled .380 ACP in the 2.5 to 2.7" range, rather than a PP or PPK sized barrel in the 3.4" to 3.9" range.
Barrel length makes far more of a difference in .380 ACP than in 9mm Para (and it's even more critical in .32 ACP where the 60 gr XTP also does well). I've noted velocity losses in the 50 to 70 fps range between the 3.9" PP and the 3.4" PPK/S and when you drop to 2.5" you're taking a round with a 1000 fps potential and reducing it to around 850 fps. That's at the low end of the effective velocity range for the 90 gr XTP and below the effective range for pretty much every other hollow point. So with a short barreled .380 ACP, it's your only viable hollow point choice.
What makes the Hornady 90 gr XTP work well in the .380 ACP is that it is only a moderately expanding bullet. On average you can expect expansion to about .53 caliber which is right at the 1.5x FBI standard so it just hits the minimum expansion needed, and that still allows maximum penetration with the available kinetic energy which means it will reliably exceed the 12" mark in a 3.5" to 3.9" .380 ACP. If you can get 850 fps out of the 90 gr XTP in your pistol, you are pretty much good to go and are far better served than you would be with an FMJ.
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With a longer barreled .380 ACP, you'd have a couple more viable options. The 102 gr Golden Saber expands to a very impressive .60 caliber with nasty, sharp edges on the jacket, but the velocity range where it will penetrate is very narrow. With too fast a muzzle velocity it will expand prematurely and come up short in the 10" range, and with not enough velocity it will expand slower but will still lack the energy needed to make it to 12", if it expands. In denim at too slow a velocity, it tends to not expand at all. For a short barrel pistol the hotter underwood loading is preferable and in a longer barrel .380 ACP the Remington load is preferable. It has it's faults in terms of penetration, but on the other hand, the full 12" is not needed in the majority of civilian self defense shoots and you can argue that 10" to .60 caliber hole is worth having.
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There is no "+P" loading for .380 ACP, just the 21,500 psi SAAMI spec. Buffalo Bore has heavy loaded ammo that they call "+ P" but it's a misnomer as there is no "+ P" standard, so it just loaded in excess of SAAMI spec.
The heavy loaded and standard loaded Buffalo Bore rounds are better than FMJs in the sense that they have a flat point that is probably more effective than a round nosed FMJ, but they are hard cast and will not expand. The same 75 grain bullet in soft cast lead actually makes more sense from both expansion and leading perspectives. Given the comparatively low pressure of the .380 ACP round a BHN of 12 is plenty and a hard cast bullet is counter productive. But marketing trumps science and engineering every time.
I don't recommend the "heavy" Buffalo Bore loads. They are harder to shoot accurately in a small .380 and the extra 4" of penetration to 21" is a total waste, so there is no upside, and significant downside. Hits count in a gun fight and I see no advantage to shooting a round that you can't practice with, and you can't practice with the "heavy" loaded BB rounds as they beat the tar out of your pistol. 100-150 rounds a week with a round with a similar recoil impulse would substantially shorten the life of your pistol, so people who use the heavy loaded BB rounds either don't practice much, or have to practice with a round that will have significantly less recoil than their carry round. That violates the train like you intend to fight principle. But the BB rounds sell well in a "faster must be better" world and the heavy BB load has avid fans.