Modern ammunition in a 380 auto gives it power squarely in the same class as a 38 special. A 38 special isn’t the biggest gun on the block but police carried 38 revolvers as duty weapons for a long long time and it seemed to work for them.
As far as the recoil goes it has to be something that has to be felt to understand. If you just look at recoil energy numbers it isn’t that much like 8 ft lbs. However I find the recoil of the 8.3 oz 380 auto to be harder to handle than that of my super redhawk 44 mag with 300 gr handloads at 1400 fps which equates to 33 ft lb or recoil or the same recoil energy as a 338 win mag rifle.