Both are quite natural and there is no way of judging which is intended; I respect you as a doctor/patient/policeman/car owner/neighbor/etc. It is a very badly written question.
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AnonymousSo I can say either one and it could mean the same in the end, right?No, not at all. We have no way of knowing who is the professor and who is the student, but all persons are capable of respect and of being respected, no matter what their station.