they usually don't perform physicals (none I know take referrals from sources other than MD's / NP's who have already performed that), but do tend to eliminate endocrine, thyroid, nervous system, etc. issues -- I've even seen them order some more esoteric tests when they thought it warranted, including specialized labs, CT's / MRI's, etc.. They also have a lot more training in monitoring side effects including medical interactions and possible true side effects -- cholesterol and liver problems, development of diabetes, treatment of thyroid issues along with psychiatric issues when warranted, etc.
In addition, the have expertise in neurology that psychologists do not -- including training in dealing with concurrent issues (dementia vs. depression or psychosis). Remember in most residencies psychiatry and neurology have the same program for the first 18 mos to 2 years.
Having worked in a CMHC, CHC's, and with a large cross section of behavioral issues from social workers, LCSW's, clinical and educational psychologists, family physicians, nurse practitioners, and psychiatrists, my vote would be to leave the physicians in charge of medical treatment -- including prescriptions. Family physicians a fair amount of training in mental health (more than psychiatric np's for instance), and are adequate for most outpatient treatment. Psychiatric NP's and internal medicine doc's don't usually have as much training, but are certainly capable of managing and monitoring based on a plan of action from a specialist. For brittle cases or inpatient care a specialist is obviously warranted.