Biden and Ryan cite their faith as a formative influence, but neither is known as a standard-bearer for the Catholic hierarchy's chief political causes: abortion and gay marriage. In fact, the two candidates are politically at least nearly polar opposites.
Biden agrees with the church on social-justice issues such as poverty, but runs afoul on gay marriage and abortion rights. Ryan, meanwhile, agrees with Catholic doctrine on abortion and gay marriage, but clashes with church leaders on social-justice issues.
With Catholics comprising nearly a quarter of the U.S. electorate and nearly a third in Midwestern swing states the "Who's the Better Catholic?" debate may become far more than an intra-church squabble.
"It has the potential to have a huge impact on this election," said Maria Mazzenga, a historian at Catholic University in Washington.
Neither the Democratic nor Republican party platforms perfectly align with the wide body of Catholic social doctrine, which encompasses views on everything from war to economics to the unborn.
"The official teachings of the church can't really be put into one camp or the other," said Mazzenga.
So Catholic politicians must often choose between church and party orthodoxy, said R. Scott Appleby, a professor of history at the University of Notre Dame.
"In our current system, is it possible to have a politician who, along with papal teaching, says no to abortion, no to nuclear proliferation, no to poverty? The answer is no," Appleby said.
Biden has said that "as a Roman Catholic, I am willing to accept the teachings of my church" on abortion. But, he continued in a 2008 "Meet the Press" interview, "for me to impose that judgment on everyone else who is equally and maybe even more devout than I am seems to me is inappropriate in a pluralistic society."
Biden, who had already been barred from speaking at Catholic schools in Wilmington because of his stance on abortion, was blasted by bishops.
Archbishop Charles Chaput, a leading voice in the church who now heads the Archdiocese of Philadelphia, called Biden's argument "morally exhausted."
"It's certainly true that we need to acknowledge the views of other people and compromise whenever possible," Chaput said at the time, "but not at the expense of a developing child's right to life."
Bill Donohue, president of the conservative Catholic League, said the hierarchy has made it clear that outlawing abortion and defending traditional marriage are the church's top political priorities.
"This puts Biden at a decisive disadvantage in making the case that he better represents Catholic teachings," Donohue said.
But conservative Catholic activist Deal Hudson argues that Ryan, too, has a "Catholic problem."
The Wisconsin congressman heads the House Budget Committee and is credited with writing the 2012 and 2013 House Republican budget plans, which call for steep cuts to programs that care for the poor, such as food stamps and Medicaid, while giving tax breaks to the wealthy.
For the past two years, the U.S. Conference of Catholic Bishops has written a series of letters to House lawmakers, including Ryan, arguing that the "central moral measure" of any budget is how it affects "poor and vulnerable people."
Ryan's 2013 budget plan, which passed in the House, but has died in the Senate, "fails to meet these moral criteria," wrote Bishop Stephen Blaire of Stockton, Calif., chairman of the bishops' Committee on Domestic Justice and Human Development.
Catholic nuns, scholars and Franciscans have been even more critical.
Nuns protested Ryan's budget on a nine-state bus tour this summer, rallying outside his district office. The Franciscan Action Network accused the congressman of "balancing the budget on the backs of the poor." Nearly 90 scholars at Georgetown University, the nation's oldest Catholic college, said that Ryan's budget owes more to Ayn Rand, whom he has cited as a major influence, than to the gospel.
Ryan has vigorously defended his budget and fidelity to Catholic social teaching.
"The overarching threat to our whole society today is the exploding federal debt," Ryan said at Georgetown in April. "The Holy Father, Pope Benedict, has charged that governments, communities, and individuals running up high debt levels are 'living at the expense of future generations' and 'living in untruth.' "
Ryan has also cited the Catholic principle of "subsidiarity" to argue that government programs should not crowd out civic life, including local charities and churches.
In a Daily Beast article, Hudson suggested that Ryan has more convincing to do.
"The bottom line," he wrote, "is this: the Romney-Ryan campaign must acknowledge the Catholic concerns about the budget as a major obstacle to winning the election."