shout down vs hush up

shout down and hush up both are verbs.

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

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

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

shout down (verb)	hush up (verb)
silence or overwhelm by shouting	cause to be quiet or not talk
	cover up a misdemeanor, fault, or error