big cheese vs big wheel

big cheese and big wheel both are nouns.

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

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

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

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