Biden -- using words including "malarkey" and showing considerable impatience at times -- frequently interrupted to challenge Ryan's debate points, while Ryan said the nation is witnessing "the absolute unraveling of the Obama foreign policy."
The first question was whether the attack on the U.S. Consulate in Benghazi, Libya, resulting in the death of U.S. Ambassador Chris Stevens and three other Americans was "a massive intelligence failure."
Biden said the Obama administration "will find and bring to justice the men who did this" and promised a full investigation.
"Wherever the facts lead us, we will make clear to the American public that whatever mistakes were made will not be made again," he said.
Ryan said the administration's handling of the matter "is becoming more troubling by the day."
"They sent the U.N. ambassador out to say this [attack] was because of a protest and a YouTube video," Ryan said. "It took the president two weeks to say this was a terrorist attack."
After Ryan criticized the administration over security arrangements for the consulate, Biden said, "With all due respect that's a bunch of malarkey because not a single thing he said was accurate."
Biden said congressional Republicans voted to cut funding for embassy security, and he criticized GOP presidential nominee Mitt Romney for making a political statement "even before we knew the ambassador killed" that was "panned by the media around the world."
"That's not presidential leadership," Biden said.
Responding to a charge the administration has told a changing story about the attack, Biden said the intelligence community changed its assessment "as they learned more facts."
"There were requests for extra security" at the consulate, Ryan said. "Those requests were not honored."
On the prospect of Iran obtaining nuclear arms, Ryan accused the Obama administration of disregarding Israeli Prime Minister Binyamin Netanyahu's concerns and allowing Iran to get closer to having a nuclear weapon.
Biden said Ryan's argument was "malarkey" and said economic sanctions on Iran are the toughest "in the history of sanctions."
Biden and Ryan agreed on withdrawing from Afghanistan, but Ryan criticized the Obama administration for making clear U.S. forces will withdraw in 2014, saying "we don't want to embolden our enemies to hold out and wait for us."
We are witnessing "the absolute unraveling of the Obama foreign policy," Ryan said.
Biden said the Afghan war has achieved its purpose and it's the Afghans responsibility to "take over their own security."
"We are leaving in 2014. Period," Biden said.
In response to a question about bringing the unemployment down below 6 percent, Biden said the administration could do it but declined to predict how long it might take. He then criticized Romney for comments the nominee made in Florida in May, saying 47 percent of Americans depend on government and don't take responsibility for their own lives.
"It's about time they take some responsibility here," Biden said of Republicans, suggesting they should sign a pledge "telling the middle class we're going to level the playing field instead of signing a pledge not to raise taxes."
Ryan pointed out U.S. economic growth has slowed in each of the past two years and job growth has slowed in the last three months.
"This is not what a real recovery looks like," Ryan said. "We need real reforms for a real recovery, and that's what Governor Romney and I are proposing."
On Medicare, Ryan said the policy he and Romney propose "preserves the program for current retirees by changing it for younger Americans."
"[Democrats] haven't put a credible solution on the table," Ryan said.
He also said the Obama administration "got caught with their hands in the cookie jar" to pay for the Affordable Care Act when it reduced total Medicare expenditures by $416 billion through cuts to supplemental coverage sold in the private market.
"We stopped overpaying" for the private coverage, Biden said.
"Folks, follow your instincts on this one," Biden said. "Their ideas are old and their ideas are bad."
The nominees were asked to describe how their personal religious views influence their policy positions on abortion.
Ryan said his opposition to abortion is not "simply because of my Catholic faith. That's a factor, of course, but it's also about reason and science."
"I believe that life begins at conception," he said.
Ryan said a Romney administration would oppose abortion with exceptions for rape, incest and saving the life of the mother.
"My religion defines who I am," Biden said. "Catholic social doctrine talks about helping those who can't take care of themselves."
Biden said he accepts his church's position that life begins at conception, "but I refuse to impose that on others, unlike my friend here, the congressman."
He said the decision to have an abortion should be left to a woman and her doctor.
Prior to the debate, Robert Gibbs, a senior adviser to the Obama-Biden campaign, said on NBC's "Today" show Biden would have to be "on his toes" in the debate because Ryan was apt to do what Romney "tried to do [in last week's presidential debate], which is [have Ryan] walk away from the positions that he's held during this campaign and try to give a much, much different and softer image for the American people."
Biden prepared for the confrontation with four days of mock debates, with U.S. Rep. Chris Van Hollen, D-Md., standing in for Ryan.
Ryan told radio station WJR, Detroit, Monday he expected Biden would come at him like a "cannonball."
Ryan began preparing for the debate shortly after the Republican National Convention ended Aug. 30, Ryan spokesman Michael Steel was quoted by USA Today as saying.
The House Budget Committee chairman had "at least eight or nine days" of practice sessions in Florida, Virginia, Wisconsin and Washington, Steel said. Theodore Olson, U.S. solicitor general under President George W. Bush, played Biden in mock debates.
The 90-minute televised debate at Centre College's 1,470-seat Newlin Hall was moderated by ABC News foreign correspondent Martha Raddatz.
Obama campaign aides denied to the Los Angeles Times that Obama's low-key debate showing last week had put performance pressure on Biden, saying the mood was light.
Obama acknowledged Wednesday he had an off-night at the Oct. 3 debate, which let Romney seize the initiative.
"I think it's fair to say I was just too polite," Obama told the syndicated "Tom Joyner Morning Show" Wednesday, adding he thought it was also "fair to say that we will see a little more activity at the next one."
That debate Tuesday is to be a "town meeting" format at a 5,000-seat sports and exhibition complex at Hofstra University near New York.
Obama later told ABC News, "Governor Romney had a good night [in the first debate] -- I had a bad night."
Romney spokeswoman Amanda Henneberg retorted Obama "had a bad four years and the American people suffered because of it."
Obama told ABC he wasn't dwelling on his Denver debate performance.
"I played a lot of sports when I was a kid, and still do," he said. "If you have a bad game, you just move on. You look forward to the next one. And it makes you that much more determined. The difference between this and sports is that the stakes are so high."