nut case vs eccentric person

nut case and eccentric person both are nouns.

Word	Noun	Adjective	Verb	Adverb
nut case	Yes	No	No	No
eccentric person	Yes	No	No	No

As nouns, eccentric person is a hypernym of nut case; that is, eccentric person is a word with a broader meaning than nut case:

Other hypernyms of nut case include eccentric, flake, geek, oddball.

nut case (noun)	eccentric person (noun)
a whimsically eccentric person	a person with an unusual or odd personality