big cheese vs head honcho

big cheese and head honcho both are nouns.

Word	Noun	Adjective	Verb	Adverb
big cheese	Yes	No	No	No
head honcho	Yes	No	No	No

As nouns, big cheese and head honcho are synonyms defined as:

Other synonyms of big cheese include big deal, big enchilada, big fish, big gun, big shot, big wheel.

big cheese (noun)	head honcho (noun)
an important influential person	an important influential person