It just depends on what you want your role to be in the program. Do you want to be running groups, providing individual therapy, performing assessments, and writing reports? Be a psychologist. Do you want to prescribe and manage medications and track and manage components of physical health? Be a psychiatrist. I don't think residential ED programs typically have a PCP, at least not full-time on staff. However, inpatient ED programs will have one or more.
By the way, where are you located and/or wanting to practice? I could give a fair amount of insight into ED programs in the Minnesota area and some in the Wisconsin area.