badness vs worse

badness and worse both are nouns.

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

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

badness: that which is below standard or expectations as of ethics or decency
worse: something inferior in quality or condition or effect

Other hyponyms of badness include unworthiness, evil, evilness, undesirability, unsoundness, liability, inadvisability.

badness (noun)	worse (noun)
that which is below standard or expectations as of ethics or decency	something inferior in quality or condition or effect
used of the degree of something undesirable e.g. pain or weather
an attribute of mischievous children

badness (adjective)	worse (adjective)
	(comparative of `bad') inferior to another in quality or condition or desirability
	changed for the worse in health or fitness

badness (adverb)	worse (adverb)
	(comparative of `ill') in a less effective or successful or desirable manner