ABC's Martha Raddatz moderated the Danville, Kentucky debate, which focused on domestic and foreign policy issues.
With less than one month until voters go to the polls, the two sparred over Libya, Iraq and Afghanistan on the foreign policy front and abortion, taxes and healthcare on the domestic.
As predicted, Biden was much more aggressive than President Barack Obama was in his first debate with Mitt Romney, seemingly determined to salvage the president's much-criticized performance last week. The evening also saw a more subdued Ryan, who came across as more centrist than on the campaign trail.
Biden and Ryan passionately voiced their opinions during a heated, free-wheeling 90 minute debate that ranged from the topic of military intervention abroad to the long term viability of Social Security, Medicare and Medicaid.
Pundits were split on the candidates' appearance and behavior during the debate. Many noted Biden's habit of smiling and laughing while Ryan was speaking. They also noted Ryan's discomfort, especially on issues of foreign policy, and his habit of drinking water on stage.
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The two were seated next to each other at a round table. That intimate format, coupled with Raddatz's engaged interaction, facilitated a passionate, sometimes combative, atmosphere.
There were a number of personal attacks between the two.
“With all due respect, that's a bunch of malarkey,” Biden said to Ryan early in the debate. He also termed Ryan's claims “a bunch of stuff.”
Ryan later dismissed Biden's comments, saying “That’s Irish.”
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Still, for the most part, the participants tempered their comments with an unusual amount of facts and figures, which for many viewers became confusing and a bit "wonkish," according to ABC News.
Ryan's long winded answers on taxes and budget structure prompted Raddatz to ask, "And you guarantee this math will add up?"
"Absolutely. Six studies have guaranteed — six studies have verified that this math adds up," Ryan responded.
Later in the debate, on several occasions, Biden referenced Romney's controversial "47 percent" remark, which Obama failed to mention last week.
Ryan, for his part, attempted to address claims his running mate's economic plans were too vague by offering a litany of numbers and figures.
After some 80 minutes of substantive talk on the issues, the candidates took a step back to respond to two highly personal questions: the importance of their shared Catholic faith and how it informs their views on abortion.
The two offered a sharp contrast in opinions.
"I believe that life begins at conception ... those are the reasons why I'm pro-life," Ryan said. "Now, I understand this is a difficult issue, and I respect people who don't agree with me on this, but the policy of a Romney administration will be to oppose abortion with the exceptions for rape, incest and life of the mother."
Biden, on the other hand, said that while he believes in the teachings of the Catholic Church, "I do not believe that we have a right to tell other people that, women, that they can't control their body. It's a decision between them and their doctor, in my view, and the Supreme Court. I'm not going to interfere with that."
Biden also said the next president could indirectly decide whether abortion remains legal in the US based on whom they appoint to the Supreme Court.
Next Tuesday, Obama and Romney will hold their second presidential debate on foreign and domestic policy in a town hall meeting at Hofstra University in New York.
Watch video of the full debate between Biden and Ryan: