cock-a-hoop vs braggart

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

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

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

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

cock-a-hoop (noun)	braggart (noun)
	a very boastful and talkative person

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