big gun vs head honcho

big gun and head honcho both are nouns.

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

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

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

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