big fish vs head honcho

big fish and head honcho both are nouns.

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

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

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

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