peace of mind vs quietness

peace of mind and quietness both are nouns.

Word	Noun	Adjective	Verb	Adverb
peace of mind	Yes	No	No	No
quietness	Yes	No	No	No

As nouns, quietness is a hypernym of peace of mind; that is, quietness is a word with a broader meaning than peace of mind:

Other hypernyms of peace of mind include quietude, tranquility, tranquillity.

peace of mind (noun)	quietness (noun)
the absence of mental stress or anxiety	the property of making no sound
	a state of peace and quiet