badness vs unworthiness

badness and unworthiness both are nouns.

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

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

badness: that which is below standard or expectations as of ethics or decency
unworthiness: the quality or state of lacking merit or value

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

badness (noun)	unworthiness (noun)
that which is below standard or expectations as of ethics or decency	the quality or state of lacking merit or value
used of the degree of something undesirable e.g. pain or weather	the quality of being not particularly suitable or befitting
an attribute of mischievous children