The concern about penetration is pretty significant, but make yourself a fair comparison. Please understand that handguns were designed as anti-people firearms - in other words, handguns are soft tissue calibers. Please forget about shooting Hondas or Toyotas or Buicks with 38 round nose lead bullets - it is neither an accurate or valid indication of the calibers ability on a soft tissue target. The same goes for the 380.
Now, under most circumstances a jacketed 380, ball or otherwise, will probably penetrate a car fender while a 38 lead round nose will probably not unless you hit it square on. The lead will deform enough to cause the bullet to glance away.
I once loaded up some 38s, semiwadcutters, to shoot through a buddy's snub nose and my 6" 357. The target was the top of a 55 gallon drum, laid on angle facing up at a distance of about 15m. The shots from the snubnose glanced or ricocheted off - only one or two penetrated as they were pretty much straight on hits whereas from the 6" 357 they all penetrated straight through. In a couple of instances the ricochetes from the snubnose came right back at us. However, those very same loads were used in a self defense shooting two years later, with complete pass throughs.
I don't know how many of you fellas have access to a junkyard - pardone moi, automative reclaimation facility, but if you can get yourself the hood of a car or even a door you can find out how your bullets penetrate. We have the hood of an older camaro at a friend's place where we are clearing trees for a building and have set up the hood for a target. The thing is fulla 22 holes, 38 holes, a bunch of Tokarev holes and even some 45 holes but everyone who has shot the darn thing has found that some round nose softer lead slugs will glance off. Even so, we now need to flip the hood over so get some less shot up target areas but still, the old addage comes back every time - don't try and stop a car with a 38. The 38 is adequate for anti-personnel work as it will stop an assailant, but it won't stop a vehicle.
You just have to understand that you need to practice with whatever it is you are carrying. Both the 38 spl and the 380 are on par with each other. Forget +P loads in either, the standard velocity, standard pressure loadings work just as well and are easier to control.
If you really want to see what a 38 or 380 will do to a carcass, get yourself a couple of old turkeys from the market - not frozen. Make certain they are thawed and line up two or three in a row and see how your different calibers and bullets perform. Please understand that a sub-sonic 22lr will completely penetrate a 10 lb turkey at a distance of 300 yds so imagine what your 38 or 380 will do at personal defense distances. Mikey.