big fish vs big gun

big fish and big gun both are nouns.

Word	Noun	Adjective	Verb	Adverb
big fish	Yes	No	No	No
big gun	Yes	No	No	No

As nouns, big fish and big gun are synonyms defined as:

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

big fish (noun)	big gun (noun)
an important influential person	an important influential person