When Chinese President Xi Jinping’s handlers arranged his flight from Seattle to Washington, D.C., on Thursday, they made sure he would land after Pope Francis had left. Xi didn’t want to be overshadowed by the rock-star pope.

As it turned out, the Chinese leader was unable to avoid the pope’s shadow. The elaborate reception ceremonies for Xi on the White House lawn were eclipsed on TV by the pope’s address to the United Nations.

But, apart from timing, comparisons between the pope and Xi are unavoidable.

The two leaders command the two largest constituencies in the world, 1.2 billion Catholics and 1.2 billion Chinese, respectively. And they hold polar opposite views on how to address the problems of their flocks and the world.

Pope Francis believes that solutions must emerge from the bottom up, while Xi seeks to solve everything from the top down.

During his U.S. trip, Francis stressed repeatedly that individuals have a moral responsibility to work together to preserve the environment, fight corruption, and ameliorate conflicts. His urgings were not just spiritual homilies but calls for grassroots political action to press legislators to act.

Citing four American heroes who turned “dreams into action” — Abraham Lincoln, the Rev. Dr. Martin Luther King Jr., Dorothy Day, and Thomas Merton — the pope made clear that individual efforts to effect change are as important as those of the political elite.

However, the pope was also concerned about the future of Western democratic institutions, many of which have become so sclerotic that they have turned voters into cynics.

As he addressed a joint session of Congress, Francis urged legislators to overcome the partisan behavior that has paralyzed our government.

Xi, on the other hand, is an authoritarian, distrustful of grassroots efforts. China experts believe his outlook stems more from personal history than Leninist ideology, which has largely given way in China to a blend of nationalism and Confucianism. Despite his family’s communist pedigree, Xi was forced to labor in the countryside for years during the chaos of the Cultural Revolution; he appears to have emerged with the belief that order must be strictly imposed from above.

So Xi has moved to quash China’s expanding civil society and its remaining free media, and shows a Mao-like propensity to rule from the very top.

What’s so fascinating is that Francis and Xi are addressing many similar problems — especially pollution and corruption — but from a totally different perspective.

The pope pleaded in Congress and at the United Nations for individual and governmental action to combat man-made climate change. Meantime, Xi proposed a cap-and-trade plan that would supposedly limit China’s greenhouse gas emissions.

Chinese action on this front is essential, as Beijing has surpassed the United States as the world’s biggest polluter.

However, it’s hard to have confidence in a Chinese government that blatantly manipulates statistics and markets, and seeks to control (and hack) the Web. When China’s stock market recently tanked, the government’s reaction was to bend the stats back into shape by forbidding press coverage, banning sales of shares, and intervening massively to fix prices.

This hardly inspires confidence in a market for cap and trade.

Similarly, Xi is waging war on Chinese corruption from the top down, by publicly firing and arresting a number of party officials. In a country as huge as China, fighting corruption from such heights is likely to fail.

On my last trip to China, I heard from senior Chinese officials that they often depend on nongovernmental agencies working on health or environmental issues to alert them to corruption far from Beijing. Ditto for the work of local Chinese media that struggle to expose provincial misbehavior at great risk.

But Xi is shutting down civil society and activist media, isolating himself and his circle. He is failing to take advantage of a growing middle class that could play a critical role in fighting pollution and exposing corruption.

In a sense, Pope Francis is daring us to demonstrate that our model is preferable to China’s. He is trying to mobilize individuals to join together to work for the common good, and legislators to act responsibly as well.

Yet, as he observed in Congress, the discontents and contradictions of U.S. democracy can thwart such efforts. All the more so if legislators make war on all regulations, including those that curb pollution or combat destructive behavior by banks.

As if to confirm Francis’ analysis, the Republican House speaker, John Boehner — a devout Catholic who had invited the pope to address the joint session — announced his resignation Friday. The conservative Boehner had been hounded by GOP extremists who seek to shut the national government down, yet again — something the speaker opposed.

The pontiff has thrown down a challenge for Americans to do better. He urged Congress to “confront every form of polarization,” and individual Americans to pursue “dreams that lead to action.”

The difference between Francis and Xi is basic: The pope believes in democracy’s endless prospects for renewal by committed individuals and legislators. We have the chance to prove him right or wrong.

Trudy Rubin is a columnist and editorial-board member for the Philadelphia Inquirer.