With Rick Perry and Mitt Romney now leading the field, the Republican 2012 presidential contest is creating a new chapter in the story of two men who have occasionally clashed and who have markedly different personal styles.

In 2006, during a meeting in Austin, Mr. Perry, the Texas governor, questioned a decision Mr. Romney, then the governor of Massachusetts, had made as chairman of the Republican Governors Association. Mr. Romney had hired the media adviser Alex Castellanos for the group, though Mr. Castellanos was working...