[Tomac]

Define "better ammo".
If talking for self-defense, all handguns are relatively poor "stoppers" regardless of caliber or bullet used. Shot placement and sufficient penetration are paramount, all else is secondary.
Using your .380 cap as an example, the cartridge simply isn't powerful enough to provide both sufficient penetration and decent expansion, so I'd choose sufficient penetration if needbe.
With more powerful cartridges it's possible to combine both sufficient penetration and decent expansion but there are exotic rounds out there (Glaser Safety Slug, MagSafe, etc) that sacrifice sufficient penetration for overexpansion resulting in nasty surface wounds that can fail to reach the vitals.
HTH...
Tomac