feast one's eyes vs relish

feast one's eyes is not a noun while relish is a noun.

Word	Noun	Adjective	Verb	Adverb
feast one's eyes	No	No	Yes	No
relish	Yes	No	Yes	No

As verbs, relish is a hypernym of feast one's eyes; that is, relish is a word with a broader meaning than feast one's eyes:

feast one's eyes: look at with great enjoyment
relish: derive or receive pleasure from; get enjoyment from; take pleasure in

Other hypernyms of feast one's eyes include bask, enjoy, savor, savour.

feast one's eyes (noun)	relish (noun)
	the taste experience when a savoury condiment is taken into the mouth
	vigorous and enthusiastic enjoyment
	spicy or savory condiment

feast one's eyes (verb)	relish (verb)
look at with great enjoyment	derive or receive pleasure from; get enjoyment from; take pleasure in