to the brim vs to the max

to the brim

prep
  • Used other than figuratively or idiomatically: see to, brim. 

  • To the point of being full, almost overflowing. 

to the max

prep
  • To a great degree or extent; very. 

  • To the maximum possible degree or extent. 

How often have the words to the brim and to the max occurred in a corpus of books? (source: Google Ngram Viewer )