Over the last 12 months, fortunes have diverged for Akio Toyoda and Takanobu Ito, the leaders of Japan's No. 1 and No. 3 carmakers.

Toyota President Toyoda is the toast of Tokyo: His company is projecting a record $18 billion profit for the year. Honda President Ito, who many view as the more visionary of the two, is out of a job. Toyota appears to have fully recovered following a major safety crisis, when its cars were blamed for unintended acceleration that led to several deaths. Honda, meanwhile, is still grappling with a scandal involving deadly airbags manufactured by Takata, as well as several of its own quality-control issues.

A common thread, however, runs through their differing trajectories: the weak yen, which has become a major pillar of Prime Minister Shinzo Abe's reform efforts.