butt heads vs cross swords

butt heads

verb
  • To argue uncompromisingly. 

  • To struggle against something that does not give way. 

cross swords

verb
  • To quarrel or argue with someone; to have a dispute with someone. 

  • Used other than figuratively or idiomatically: see cross, sword., to place or hold two swords so they cross each other. 

  • For males, to urinate simultaneously such that the streams intersect. 

  • To fight with someone; to duel. 

How often have the words butt heads and cross swords occurred in a corpus of books? (source: Google Ngram Viewer )