big shot vs high muckety-muck

big shot

noun
  • A person with a reputation of importance or power. 

  • A rare and significant chance to achieve fame or success. 

high muckety-muck

noun
  • Synonym of high muckamuck. 

How often have the words big shot and high muckety-muck occurred in a corpus of books? (source: Google Ngram Viewer )