incompetence vs inability

incompetence and inability both are nouns.

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

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

Other hypernyms of incompetence include unfitness.

incompetence (noun)	inability (noun)
lack of physical or intellectual ability or qualifications	lacking the power to perform
inability of a part or organ to function properly	lack of ability (especially mental ability) to do something