undesirability vs badness

undesirability and badness both are nouns.

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

As nouns, badness is a hypernym of undesirability; that is, badness is a word with a broader meaning than undesirability:

undesirability: the quality possessed by something that should be avoided
badness: that which is below standard or expectations as of ethics or decency

Other hypernyms of undesirability include bad.

undesirability (noun)	badness (noun)
the quality possessed by something that should be avoided	that which is below standard or expectations as of ethics or decency
	used of the degree of something undesirable e.g. pain or weather
	an attribute of mischievous children