big cheese vs heavy hitter

big cheese

noun
  • A very important figure, especially a high-ranking person in an organization. 

heavy hitter

noun
  • A person of considerable importance who is a major decision maker or capable achiever; an especially significant organization or an especially functional object. 

  • A player with a favorable batting average who is especially good at hitting the ball deep into the outfield or farther. 

  • In any sport, a strong, physical player who is particularly effective. 

How often have the words big cheese and heavy hitter occurred in a corpus of books? (source: Google Ngram Viewer )