I think there are some situations where one or the other more definitely fits. One one end of the spectrum, a schizophrenic inpatient or someone receiving therapy for mental illness from a psychiatrist, patient is pretty appropriate. On the other end, there are people are not in fact mentally ill but seeking therapy for other reasons. ie marital counseling....I think calling the couple patients could be offensive.

My therapist was a psychiatrist. She didn't use the terminology one way or another most of the time. when she did it was usually "patient". It didn't bother me. As I work in medicine too, patient is a familiar term/relationship and it wasn't demeaning or offensive to me in anyway. It didn't feel like she was being overly paternal or anything.