big deal vs big gun

big deal and big gun both are nouns.

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

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

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

big deal (noun)	big gun (noun)
anything of great importance or consequence	an important influential person
an important influential person