Don't think that the .380 will have less recoil. Between the two cartridges, there is a difference in the size of the pistol, with the 9mm being a bit larger. So when all is considered, they end up having nearly identical recoil in pocket guns.
Obviously. If sizes are held roughly constant, however, .380 has noticeably less recoil, e.g., comparing the LC9 with the Glock 42. The 42 is even a bit lighter, and still has less felt recoil.
