big shot vs big deal

big shot and big deal both are nouns.

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

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

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

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