big deal vs big shot

big deal and big shot both are nouns.

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

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

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

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