bragging vs cock-a-hoop

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

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

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

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

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

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