high dudgeon vs outrage

high dudgeon and outrage both are nouns.

Word	Noun	Adjective	Verb	Adverb
high dudgeon	Yes	No	No	No
outrage	Yes	No	Yes	No

As nouns, outrage is a hypernym of high dudgeon; that is, outrage is a word with a broader meaning than high dudgeon:

high dudgeon: a feeling of intense indignation (now used only in the phrase `in high dudgeon')
outrage: a feeling of righteous anger

Other hypernyms of high dudgeon include indignation.

high dudgeon (noun)	outrage (noun)
a feeling of intense indignation (now used only in the phrase `in high dudgeon')	the act of scandalizing
	a wantonly cruel act
	a disgraceful event
	a feeling of righteous anger

high dudgeon (verb)	outrage (verb)
	strike with disgust or revulsion
	force (someone) to have sex against their will
	violate the sacred character of a place or language