head honcho vs big gun

head honcho and big gun both are nouns.

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

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

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

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