A 357 or 9mm out of a short derringer barrel is no better than a 38.
I have a Bond CA Papa Bear model in 45 Colt. The CA models do not chamber a 410 shell and have a lot more rifling in the barrels. I carry it with Buffalo Bore heavy standard pressure load @ 1100 fps ... out of the Bond Papa Bear it's more like 800-900 fps which is right in there with a full-sized 45 ACP. And the stopping power of a 45 ACP is legendary. Recoil with this load is not bad at all. I will take two rounds of 45 ACP over five rounds of 38 special any day of the week. 380? Don't make me laugh. With either, if the perp has a gun he can easily kill you after you've shot him before he goes down. A 45 ACP center mass will put him down instantly. I have no problem at all keeping both shots center body mass at 15 yards.
Self-defense, to me, is a last-resort up close and personal affair. In a serious up close attack, you aren't going to have time for more than two rounds anyway. You want something that will STOP the S.O.B. in his tracks instantly. I also have a Kahr MK40 Elite ... six rounds of 40 S&W. But it's double action only and I just do NOT feel safe carrying a round in the chamber, so to get it into action I have to rack the slide. I can get the Bond derringer into action much faster. And let's face facts ... no matter what, if you ever have to use a gun, your life is going to be a mess for a while and if you say the wrong thing, your butt will end up in jail. Two rules: 1 - Never pull a gun unless you know you're going to USE it. 2 - If you do have to use it, make sure you KILL the bastard so he can't bankrupt you with law suits afterwards.
At any rate, my Bond 45 Colt derringer is my preferred CC gun.