neglect of duty vs negligence

neglect of duty and negligence both are nouns.

Word	Noun	Adjective	Verb	Adverb
neglect of duty	Yes	No	No	No
negligence	Yes	No	No	No

As nouns, negligence is a hypernym of neglect of duty; that is, negligence is a word with a broader meaning than neglect of duty:

neglect of duty: (law) breach of a duty
negligence: failure to act with the prudence that a reasonable person would exercise under the same circumstances

Other hypernyms of neglect of duty include carelessness, neglect, nonperformance.

neglect of duty (noun)	negligence (noun)
(law) breach of a duty	failure to act with the prudence that a reasonable person would exercise under the same circumstances
	the trait of neglecting responsibilities and lacking concern