head honcho vs big shot

head honcho and big shot both are nouns.

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

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

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

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