Where a good anthropology objectively describes (aspects of) the human being, there a biblical anthropology assesses a diagnosis of the problem called 'mankind'. Anthropology means 'knowledge of the human being' and therefore a Christian should not ommit what the Bible has to say about the subject.
Personally I would ascribe the study of human character, except behavior, to anthropology, as well as the cultural differences between peoples, nations, and various groups. But those are not, directly, the subject of an ethical anthropology. Yet the Bible also holds entire nations responsible for their behavior and one day will call them to justice. And though their behavior is primarily the subject of some kind of mass psychology, national character should be the study of a Christian ethnical anthropology.
My anthropological charts are the field of theoretical anthropology, but an anthropology of ethics deals with the ethical assessment of the main opinions about what the human being is all about.