incompetency vs inability

incompetency and inability both are nouns.

Word	Noun	Adjective	Verb	Adverb
incompetency	Yes	No	No	No
inability	Yes	No	No	No

As nouns, inability is a hypernym of incompetency; that is, inability is a word with a broader meaning than incompetency:

Other hypernyms of incompetency include unfitness.

incompetency (noun)	inability (noun)
lack of physical or intellectual ability or qualifications	lacking the power to perform
	lack of ability (especially mental ability) to do something