I looked at both, but decided to get the BG380. I was looking for a pocket pistol and preferred the BG380s double action and long trigger pull to the P238s single action.
I figured a lot can go on in a pocket, between putting your hands in it, accidentally putting another item like keys into the same pocket as the gun and just general movement. I wasn't comfortable with the P238 locked and cocked with a single safety riding in my pocket. I could carry with the hammer down, and one in the chamber, but I found that I couldn't reach the hammer with my strong hand, so it would take an extra movement and both hands to make the gun ready to fire. The same would be true for carrying without one in the chamber and racking the slide after drawing.
The BG380 is double action only and has a long trigger pull. I felt much more comfortable carrying it in my pocket with one in the chamber. I debated carrying it with or without the safety on, but its easy enough to hit when drawing so I've been using it. Be aware that in addition to a long trigger pull, the trigger reset is very long too. I thought this may be an issue, before shooting it but it hasn't been so far.
I never shot the P238, but I found the BG380, while tiny, is comfortable to shoot and seems fairly accurate at short range.
Be aware, my entire opinion here is based on carrying the gun in a pocket. If I was going to be using a belt holster I might have made a different decision.