public eye vs prominence

public eye and prominence both are nouns.

Word	Noun	Adjective	Verb	Adverb
public eye	Yes	No	No	No
prominence	Yes	No	No	No

As nouns, prominence is a hypernym of public eye; that is, prominence is a word with a broader meaning than public eye:

public eye (noun)	prominence (noun)
a focus of public attention	relative importance or fame
	something that bulges out or is protuberant or projects from its surroundings
	the state of being prominent: widely known or eminent