I reload for my Taurus .380 and use both cast(my own-95gr round nose and "store bought" lead and jacketed in 92 to 115 gr. variations.
All shoot fine. You may need to "play" with the right for you charges of powder as I have loaded for both plinking/playing with lighter loads and a bit stouter loadings with jacketed hollow points for business.
No problems with any of it to date.
That little gun is pleasant to shoot and I like the trigger-easy to keep groupings at 7 yards all in the center 3 inches and that is as good as my old eyes can do
Gary
edited because I transposed 308 for 380 ooops!