head honcho vs big cheese

head honcho and big cheese both are nouns.

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

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

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

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