Not much, if any - it really depends on the loads involved.

The .380 ACP takes a significant hit in a short barrel, but you get get FBI minimum penetration and expansion with 90 gr XTPs in the 3.5" PPK or PPK/S barrel.

The .38 Special and .38 +P loads however also take a serious hit in a short barrel. It's not uncommon to lose 150-200 fps in a 1 7/8" barrel compared to a 4" barrel, and the +P load ends up being needed to elevate 1 7/8 to 2 1/8" snub nose performance to acceptable levels.

If you look at data on actual shoots, the best performing .380 ACP loads outperform all the standard pressure .38 loads in a 2" barrel, while the best of the +P .38 loads in a 2" snub nose are on par with the .380 ACP in a 3.5" PPK/S or 3.9" PP length barrel.