While I do carry a pocket .380 (Sig 238), it's loaded with FNFMJ; I don’t trust any .380 JHP to both expand and penetrate deeply enough (sure, some will get to just over 12” regularly, but that's the minimum...14-16” is my preferred depth).
My J-frames are loaded with either the classic 158gr +P SWCHP (“FBI Load” for my steel 36’s) or 125-130gr+P JHP's (Gold Dots, Golden Sabers, or PDX1 in my airweight 360 M&P, 442, or 642).
Of course, there’s also the magnum 640 & 60...those get 125gr magnum JHP’s. The steel frame handles the recoil just fine, I don’t find them to be too heavy for pocket carry, and there’s really no argument about how effective the 125gr magnum load is.
I give the edge to the .38, by the way (leaving the magnum out of the equation). I think it's a better round, for the main reason of being able to run bullets over 50% heavier than the .380; and, given how both can be expansion challenged, can run a sharp shouldered SWC or WC for a full-profile wound channel and get proper penetration.