As I recall for a period of about ten years, a certain gun magazine did alternate articles:
A: Revolvers vs Simi Autos
B: .380 vs 38
The result of article B was they were close. The 38 was the standard LEO caliber for much of America during the 20th Century. Some of those officers had violent confrontations with bikers & people with down jackets and even 3 piece wool suits and a top coat on and won. Leather is not titanium. It can be pierced with a ice pick or even a needle. Visit your local shoemaker for verification. Try on a leather jacket and look in the mirror and ask yourself "Am I bulletproof in this?". Do a Google search on "leather jacket stops bullet" and your going to find a lot of examples of it failing miserably.
In short being giving the choice of being the person with the leather jacket or being the person firing the .380, I'd opt to be the latter EVERY time.