favorite vs rival

favorite and rival both are nouns.

Word	Noun	Adjective	Verb	Adverb
favorite	Yes	Yes	Yes	No
rival	Yes	Yes	Yes	No

As nouns, rival is a hypernym of favorite; that is, rival is a word with a broader meaning than favorite:

Other hypernyms of favorite include challenger, competition, competitor, contender.

favorite (noun)	rival (noun)
something regarded with special favor or liking	the contestant you hope to defeat
a special loved one
a competitor thought likely to win

favorite (adjective)	rival (adjective)
preferred above all others and treated with partiality	as a rival in a competition
appealing to the general public

favorite (verb)	rival (verb)
To mark an item as a personal favorite on social media	be the rival of, be in competition with
	be equal to in quality or ability