badness vs naughtiness

badness and naughtiness both are nouns.

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

As nouns, badness and naughtiness are synonyms defined as:

Other synonyms of badness include mischievousness.

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