I've carried both .38s and .380s. Often I carried both at once. One as a primary and one as a spare. Previously I carried two .38s instead. One a six shot in 4 inch and one a 5 shot in two. For me it was about weight and concealment.
Some people believe their second gun should be loaded as hot as possible. If that works for them, fine. It didn't work for me. My little Smiths or Charters would just twirl like a top in my hand when fired with hot +P loads. Sure you could put a bigger grip on them, but now you are sacrificing or compromising the concealment. Early on I watched a few autopsies and interviewed enough survivors to develop confidence that where the bullet hits is a lot more important than the pocket cannon shell that missed a vital spot is. I once interviewed a person who had been shot 5 times in the chest and abdomen with a KG-99 loaded with hollowpoints at point blank range. He then took the gun away and literally beat his attacker to death with his own gun. Given the shooting victims own impressive criminal history Arlington, VA charged him but it was dismissed of course.
Bullets work in only three ways. Either a major nerve cluster is destroyed, or a vital organ is destroyed, or the subject slowly bleeds out. As shown above, he can kill you in the time it takes to bleed out. For myself, I decided accuracy of placement was a lot more important than where the load sat on the Taylor scale. My small .38s had wadcutters or standard velocity 158 grain loads in them. I eventually safequeened the snub noses for a Colt 1908 .380. Later replaced by first an old German WW2 Walther PPK (sold) and then a stainless Colt Mustang. Testing by me had determined the .38 penetration in phone books and old lumber was 'bout the same as the .380s. Neither the .38 nor the .380 would be my normal first choice if I was carrying just one pistol today, but if I had to choose between a snubbie .38 loaded with standard non +P ammo or a reliable .380 for concealment carry I would go with the .380 with a second magazine tucked away. Reasons being it is easy to shoot accurately, the bullet performance in people is about the same, and the .380 being flatter is a lot easier to conceal.
[Long ago there was a saying about African Water Buffalo, they were very easy to kill, the problem was it often took them 20 minutes to realize they were dead. This is because their vital spots were both few and well protected. This resulted in an animal requiring both maximum power and superb accuracy if one wished to survive the hunt.]