disobedience vs badness

disobedience and badness both are nouns.

Word	Noun	Adjective	Verb	Adverb
disobedience	Yes	No	No	No
badness	Yes	No	No	No

As nouns, badness is a hyponym of disobedience; that is, badness is a word with a more specific, narrower meaning than disobedience:

Other hyponyms of disobedience include mischievousness, naughtiness.

disobedience (noun)	badness (noun)
the failure to obey	that which is below standard or expectations as of ethics or decency
the trait of being unwilling to obey	used of the degree of something undesirable e.g. pain or weather
	an attribute of mischievous children