Would I carry a 380 for self defence?
yes, I would and do. Most often it is as a backup to my 1911 or my Glock 23 but I have, on occasion, carried it solo. Is it as good as a 45, 40, or even a 9mm, no. Is it better than a knife or a sharp stick , yes. The big upside is that in a package like the Kel-tec, LCP or, Tcp, it is as easy to conceal as a lot of pocket knives. Also, while some of the newer rounds are on par with, or approaching 38 special ballistics, my LCP holds seven rounds, while my much bulkier S&W J-frames only hold five. Carrying a reload for the LCP incredibly easy, while carrying a speed loader for the J-frame isn't.
The bottom line for me is that I can carry one or even two LCPs while wearing just a pair of shorts. Yes, I have two. I can put all seven rounds in the 8 ring of a B27 target with either hand, quickly. The first rule of gunfighting is to have a gun. The second is to have enough gun. While I prefer to carry a 1911 in 45acp or a Glock 23 in 40, I have no use for 9mm any more, I prefer to always have a gun. If the LCP is all I can carry, so be it. It still beats a sharp stick.
The debate can not be truely resolved
I remember when the debate was between the 9mm and the 45 ACP. There are many examples where each was adequate and other cases when it was not. All things being equal, the larger hole made by the heavier bullet wins... usually.
I have been a 45 ACP fan for many years, but often the clothes I wear does not allow me to easily conceal a large handgun. Today, my full sized holster gun is a Glock 20 in 10 mm. It is usually too large to carry and I often carry a Kahr P380. I do not feel particularly well armed, but I am also not helpless.
During my years in the Army, I usually carried a 5.56 mm NATO rifle and sometimes also a 40 mm grenade launcher. The handgun did not compare favorably with this combination. A handgun was better than nothing, but it would be easily outgunned against the AK47 or SKS rifles. A machine-gun in 7.62 mm outgunned all of the rifles and handguns. A 50 Cal machine gun was better yet... it can go on and on.
The best weapon you carry is going to be a compromise. You can tilt the scale in your favor by training and learning to maneuver in your environment. It helps to have situation awareness. Also, do you really need to get a loaf of bread at 3:00 AM? Have you trained drawing and firing your weapon at speed? Practicing things without training only means you have more to unlearn. Have you trained in conditions similar to the environment in which you may engage an enemy.. and remember, this is an enemy already engaged in an attack. That already creates a disadvantage because you are forced into reaction mode in an unfortified fighting position.
Anyway, something is better than nothing only if you know what to do.