psychopath vs mental case

psychopath and mental case both are nouns.

Word	Noun	Adjective	Verb	Adverb
psychopath	Yes	No	No	No
mental case	Yes	No	No	No

As nouns, mental case is a hypernym of psychopath; that is, mental case is a word with a broader meaning than psychopath:

psychopath: someone with a sociopathic personality; a person with an antisocial personality disorder (`psychopath' was once widely used but has now been superseded by `sociopath')
mental case: a person suffering from neurosis

Other hypernyms of psychopath include neurotic, psychoneurotic.

psychopath (noun)	mental case (noun)
someone with a sociopathic personality; a person with an antisocial personality disorder (`psychopath' was once widely used but has now been superseded by `sociopath')	a person suffering from neurosis