brag vs come out with

brag

verb
  • To boast of something. 

  • To boast; to talk with excessive pride about what one has, is able to do, or has done; often as an attempt to popularize oneself. 

noun
  • A boast or boasting; bragging; ostentatious pretence or self-glorification. 

  • The thing which is boasted of. 

  • The card game three card brag. 

adj
  • Excellent; first-rate. 

come out with

verb
  • To say something unexpected. 

  • To make something public or available to the public. 

How often have the words brag and come out with occurred in a corpus of books? (source: Google Ngram Viewer )