braggart vs cock-a-hoop

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

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

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

Other synonyms of braggart include big, boastful, bragging, braggy, crowing, self-aggrandising, self-aggrandizing.

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

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