badness vs unsoundness

badness and unsoundness both are nouns.

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

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

badness: that which is below standard or expectations as of ethics or decency
unsoundness: not mentally or physically healthy

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

badness (noun)	unsoundness (noun)
that which is below standard or expectations as of ethics or decency	not mentally or physically healthy
used of the degree of something undesirable e.g. pain or weather	a misconception that is fallacious and not true or valid
an attribute of mischievous children	a condition of damage or decay