The .380ACP is considered by most gun culture people to be a BUG caliber or one you might be inclined to carry when you cannot carry anything else for whatever reason (I have done this myself). While certainly better than a hammer, most people are not of a mind to get ventilated by anything, you are better off with a more powerful cartridge as a primary carry caliber.
That said, if you are faced with a situation as you have outlined in your post, you would be better off trying to hit the offender's nose or the area immediately around it. A large man wearing a leather jacket who is bent on doing you harm is almost certainly not going to be stopped by CM hits from a .380 unless you get lucky. What resides behind the nasal area is the medulla oblongata. A hit there will drop him post haste. But then again, that's one heck of a hard target to hit in the extreme conditions of a violent encounter. Much better to be carrying more serious firepower when and where you are able.