Xi Jinping and Jorge Mario Bergoglio would seem like natural enemies. The Chinese president runs a government that squashes religious freedom, limits procreation and has a dismal human-rights record. Bergoglio — better known as Pope Francis — wants access to Xi's many citizens in order to spread the Catholic Church's teachings, challenge the Communist Party's hold on dogma and even reach out to North Korea.

Yet these world leaders should really be sharing notes. The tasks facing the two men who took office just one day apart in 2013 are surprisingly similar — and not just because both lead flocks that number more than 1 billion people each, notes Stephan Richter, publisher of online magazine the Globalist.

"This is only where the stunning parallels start," writes Richter. "China's Communist Party and the Catholic Church share more than certain organizational characteristics, including being heavily male-dominated power structures. In addition, they both offer up ideologies or faith systems with an absolutist claim. That isn't an easy proposition in an era when fewer and fewer people are inclined to adhere to such rigid propositions."