mentally ill vs unsound

mentally ill and unsound both are adjectives.

Word	Noun	Adjective	Verb	Adverb
mentally ill	No	Yes	No	No
unsound	No	Yes	No	No

As adjectives, mentally ill and unsound are synonyms defined as:

Other synonyms of mentally ill include unstable.

mentally ill (adjective)	unsound (adjective)
suffering from severe mental illness	not sound financially
	not in good condition; damaged or decayed
	suffering from severe mental illness
	containing or based on a fallacy
	physically unsound or diseased
	of e.g. advice