shout down vs shut up

shout down is not an adjective while shut up is an adjective.

Word	Noun	Adjective	Verb	Adverb
shout down	No	No	Yes	No
shut up	No	Yes	Yes	No

As verbs, shut up is a hypernym of shout down; that is, shut up is a word with a broader meaning than shout down:

Other hypernyms of shout down include hush, hush up, quieten, silence, still.

shout down (adjective)	shut up (adjective)
	closely confined

shout down (verb)	shut up (verb)
silence or overwhelm by shouting	cause to be quiet or not talk
	refuse to talk or stop talking; fall silent
	place in a place where something cannot be removed or someone cannot escape