dirty linen vs dirty laundry

dirty linen and dirty laundry both are nouns.

Word	Noun	Adjective	Verb	Adverb
dirty linen	Yes	No	No	No
dirty laundry	Yes	No	No	No

As nouns, dirty linen and dirty laundry are synonyms defined as:

dirty linen and dirty laundry: personal matters that could be embarrassing if made public

dirty linen (noun)	dirty laundry (noun)
personal matters that could be embarrassing if made public	personal matters that could be embarrassing if made public