head honcho vs big fish

head honcho and big fish both are nouns.

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

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

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

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