Both have and are used in different bird products. One could class them based on their source and therefore, which Parrot(s) would benefit from one over the other. With that as a base, Old World Parrots would source match with Red Palm Oil, where Coconut Oil would be a slightly better choice with New World Parrots.
In truth, regardless of source, Less is Better. We use a few drops over the course of a Month.