big gun vs big wheel

big gun and big wheel both are nouns.

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

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

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

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