Typically smaller in regards to patients than a public hospital, a private mental hospital is staffed and operated by a group of private medical providers and has (usually) a higher staff to patient ratio than similar public facilities. It more often than not offers more specialized and intensive care over the chronic care of a public facility.
PRIVATE MENTAL HOSPITAL: “When the family finally got together to talk the situation over, they decided that Phyllis should be in a private mental hospital.”