pet peeve vs complaint

pet peeve and complaint both are nouns.

Word	Noun	Adjective	Verb	Adverb
pet peeve	Yes	No	No	No
complaint	Yes	No	No	No

As nouns, complaint is a hypernym of pet peeve; that is, complaint is a word with a broader meaning than pet peeve:

pet peeve (noun)	complaint (noun)
an opportunity for complaint that is seldom missed	an expression of grievance or resentment
	(formerly) a loud cry (or repeated cries) of pain or rage or sorrow
	(civil law) the first pleading of the plaintiff setting out the facts on which the claim for relief is based
	(criminal law) a pleading describing some wrong or offense
	an often persistent bodily disorder or disease; a cause for complaining