a 380 will kill a man with about the same effectiveness as a 44 magnum, within 20% IIRC for one or the other and you assume room temperature.
I don't know where you get the "within 20% figure", but accepting it for now, 20% seems a significant difference to me.
I believe a .380 will kill a small animal, e.g. rabbit, as well as a .44 Magnum. At some point, it is hard to tell the difference between sufficiently lethal and exceedingly sufficiently lethal.
But whitetail deer and people are about the same size. Granted, deer are stronger and "tougher" for their weight, but they are not much differently constructed around the heart/lung area. Would you just as soon hunt deer with a .380 as with a .44 Magnum?