fall away vs go away

fall away and go away both are verbs.

Word	Noun	Adjective	Verb	Adverb
fall away	No	No	Yes	No
go away	No	No	Yes	No

As verbs, go away is a hypernym of fall away; that is, go away is a word with a broader meaning than fall away:

Other hypernyms of fall away include disappear, vanish.

fall away (verb)	go away (verb)
fall to a lower standard	get lost, as without warning or explanation
diminish in size or intensity	go away from a place
	move away from a place into another direction
	become invisible or unnoticeable