greatness vs importance

greatness and importance both are nouns.

Word	Noun	Adjective	Verb	Adverb
greatness	Yes	No	No	No
importance	Yes	No	No	No

As nouns, importance is a hypernym of greatness; that is, importance is a word with a broader meaning than greatness:

greatness: the property possessed by something or someone of outstanding importance or eminence
importance: the quality of being important and worthy of note

greatness (noun)	importance (noun)
the property possessed by something or someone of outstanding importance or eminence	the quality of being important and worthy of note
unusual largeness in size or extent or number	a prominent status