big shot vs head honcho

big shot and head honcho both are nouns.

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

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

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

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