big wheel vs big cheese

big wheel and big cheese both are nouns.

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

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

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

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