cock-a-hoop vs crowing

cock-a-hoop is not a noun while crowing is a noun.

Word	Noun	Adjective	Verb	Adverb
cock-a-hoop	No	Yes	No	No
crowing	Yes	Yes	No	No

As adjectives, cock-a-hoop and crowing are synonyms defined as:

Other synonyms of cock-a-hoop include big, boastful, braggart, bragging, braggy, self-aggrandising, self-aggrandizing.

cock-a-hoop (noun)	crowing (noun)
	an instance of boastful talk

cock-a-hoop (adjective)	crowing (adjective)
exhibiting self-importance	exhibiting self-importance