big gun vs brass hat

big gun

noun
  • A large artillery gun or one of the largest-caliber naval guns (as on a battleship). 

  • A person, group, thing, or course of action that is powerful, influential, or particularly effective. 

brass hat

noun
  • A high-ranking officer. 

How often have the words big gun and brass hat occurred in a corpus of books? (source: Google Ngram Viewer )