In The Playboy of the Western World by J. M. Synge, Christy Mahon and Shawn Keogh are both portraits of Irish stereotypes, with Shawn being the pious coward, subordinated to the church and Christy the blustering arrogant "playboy". On the surface, what they both have in common is subordination, Christy to his father and Shawn to the Church. When Christy thinks he has killed his father, he takes on the role of a "playboy", but the role is temporary and he returns to his father power when it turns out his father is alive. This suggests a cycle in which, when Old Mahon dies, Christy will marry and father his own sons and bully them in an cycle passed down through generations. Because the Church is a long-lived institution, Shawn will never escape its shadow, and thus remain bullied rather than bullying.
The other thing the two men have in common is attraction to Pegeen.