Lets look at a common self defense round: the Speer Gold Dot. Their 90gr .380 loading is factory rated at 216FPE at the muzzle. Their regular 125gr .38+P is rated at 248. So you have a about a 15% difference. If you go with the 135gr "short barrel" .38+P loading (a good idea in a small snub) it is factory rated at 222FPE, less than a 3% difference. Of course, I do like that revolver rounds traditionally have a much wider hollow point since they don't have feeding issues to be concerned with and can use more radical HP designs.
Different ammo makers will of course have different specific measurements. Bottom line, the .380 will be a little weaker in most cases than comparable .38+P (and quite similar to non+P .38spl or more downloaded .38+P). The revolver round may have better bullet designs as well. However, the difference is pretty close, and the LCP has a definite capacity advantage. The 6+1 capacity of the LCP gives you a 20% advantage over a 5-shot snub if you run it with 6 rounds and do not top off the mag after chambering a round, if you do top off the mag and run it with 7 rounds you have a 40% capacity advantage with the LCP.
Personally, I have a small lightweight snub (the 442) and a heavier snub (a Taurus 85CH) in my rotation. I do see a definite place for them. I also have my LCP. I trust both the .38spl and .380 in pocket pistols. Now, when I can go a little bigger (IWB) I either go with an auto in at least 9mm, or I go with the steel framed snub (Taurus 85CH).