big cheese vs big shot

big cheese and big shot both are nouns.

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

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

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

big cheese (noun)	big shot (noun)
an important influential person	an important influential person