exceed vs go one better

exceed

verb
  • To go beyond (some limit); to surpass; to be longer than. 

  • To be better than (something). 

  • To be larger, greater than (something). 

  • Your password cannot exceed eight characters. 

  • To predominate. 

go one better

verb
  • To outdo somebody; to do something that surpasses what came before. 

  • To take a bet and add another to it. 

How often have the words exceed and go one better occurred in a corpus of books? (source: Google Ngram Viewer )