Shallow penetration.
In my opinion, a Hydrashok would be a better choice if you must have JHP. The 380 Hydrashok tends to expand into the .44"-.48" or so range, which means it tends to penetrate around 10-12", which is deeper than most 380 JHPs. Yes, it's a hydrashok and will fail to expand with intermediate barriers.....but that's not really a problem in this context, given the other "responsible" choice is a FMJ.
I see no reason to use the HST over the Hydrashok in 380.