As far as the chambering alone, I'm in the .38 is superior to the .380 camp. More energy, more weight, better penetration. However, which is better depends very much upon the gun you are using it in, and you.
While the .38+P has about 20% greater energy (though only about 40-50 pounds of energy), typically 20-50% greater weight, and both are generally considered the minimum for a defensive load, the differences in the guns make the deciding difference to me.
Revolvers v. autos. There are fierce battles online about which is superior. Both offer advantages over the other. If you have a strong preference of one v. the other, I don't believe the differences in the cartridges are enough to override that. Go with the type of gun you prefer, no need to even look at the other considerations. If you like both, then continue your analysis.
In general, a snub is harder to master than an auto. The 2" small frame snub has a short sight radius and a relatively stout recoil. If you go with a pocketable aluminum or lighter weight alloy, the recoil can be outright punishing with +P ammo. However, the very small pocket .380s (like the LCP) are not easy recoiling either, and some have nearly non-existent sights that are no easier to master than a snub.
If you are looking at IWB or belt carry, I would go with a .38 revolver over a PPK size/weight or larger .380. While an auto is flatter, I find a small steel frame 5-shot snubby to completely disappear IWB and it carries quite comfortably. Move up to a 3" small frame (like the S&W J-frames) or 3" medium frame (like the K-frames) and the longer barrel gives more velocity (and thus energy) and a longer sight radius, yet they still carry pretty well. While today's autos are pretty reliable, revolvers are usually a little more so (especially compared to the smaller autos). If you really like autos, in this size I don't see any advantage to a .380 and I'd go with a small 9mm over the .380 (in fact, I did: I have a SIG P290RS and a Kel Tec Pf-9, I sold my Bersa Thunder .380 long ago).
For pocket carry, I prefer an auto. Some see the flatter and sometimes smaller auto as a concealment advantage, I do not. The small autos' sharp, squared off corners, look very much like the outline of a gun in a pocket, while the multiple lumps of a revolver just look like you have stuff in your pocket. However, the small autos are much easier to shoot accurately, and are more comfortable to shoot (allowing more range practice which can mean more accuracy, and also allowing quicker follow-up shots). The only issue I have with my Ruger LCP are the sights- I should have either bought another small .380 or went with the version that comes with a laser sight (I will probably add an aftermarket laser).