I think Ryan had the advantage on substance and style. In a national race where both guys are second runner-up, this is effectively a draw for how it plays into the larger campaign narratives.

Margaret Hoover is the author of "American Individualism: How a New Generation of Conservatives Can Save the Republican Party."

William Howell: Ryan's challenge was bigger, and he met it

No great surprise, Joe Biden delivered tonight. On the heels of his boss' withering performance last week, the vice president demonstrated his deep knowledge of domestic and foreign policy issues, fluidly maneuvering between minutiae about tax policy and the draw-down in Afghanistan on the one hand and meta-arguments about the stakes involved in this election on the other. He also scored his share of style points.

Though all that laughing through those big pearly whites proved a bit unnerving at times, Biden exhibited his relish for a good debate and his conviction in essential liberal principles. The Democratic base is surely pleased.

It was Paul Ryan, though, who faced the bigger challenge. Ryan had to prove his commitment to ideas and principles that are not entirely of his choosing. During the primaries, when Romney was brandishing his conservative credentials, this task would have been easily met. But going into this debate, it was not clear that the darling among the conservative right would be able to square his views with those of the more moderate incarnation of the former governor of deep-blue Massachusetts. But well he did.

Disciplined, substantive and on point, Ryan effectively thwarted efforts by Biden to drive a wedge between the congressman's former voting record and the policy positions of the Romney-Ryan ticket. He performed as well as his party could possibly have hoped.

This debate is not likely to move the polls much at all. But that is not to say that it is entirely inconsequential. For at least the coming week, Democrats can now talk about something other than their president's detachment. And Republicans generally, but Romney in particular, can rest assured that the GOP presidential ticket is in order as they settle on a consistent message to push through Election Day.

William Howell is the Sydney Stein professor in American politics at the University of Chicago.

Maria Cardona: Pressure is on the next two debates

This was one of the best vice presidential debates I've seen. The pressure was on Vice President Joe Biden to deliver a great performance -- and deliver he did.

Biden was assertive and aggressive, and he didn't let any untruth or distortion coming out of Paul Ryan's mouth slide.

From Medicare to taxes to Iran to Afghanistan to the 47% to abortion, Biden did not miss an opportunity and was as clear as he could have been on how President Obama would be on the side of middle-class families, seniors, women and those most vulnerable in our society. He was factual and specific. His years of experience in the Senate showed as he commanded the stage with his expertise.

Rep. Paul Ryan held his own, didn't make any mistakes and was prepared. But he was outwitted by Biden and challenged by the moderator Martha Raddatz when he was being vague.

Ryan's weakest moments came when he was pressed for specifics. He seemed demure on the issue of what loopholes he would close or how he and Mitt Romney would pay for the tax cuts and defense spending increases they are proposing. Raddatz pushed him on these points, and he did not have a satisfactory answer. In some instances, whether it was on economic issues or Iran, Ryan was not able to say what he and Romney would do differently.

Biden came across as more authentic, much more passionate and as a guy who is a real champion of the middle class. Moreover, Biden was able to stop the bleeding, get Democrats excited about the next two debates and inject some much needed energy and optimism coming out of the doldrums from last week's presidential debate.

Did the debate change any minds? Probably not. It seems Republicans are happy with Ryan's performance just as Democrats are happy with Biden's.

What this means is that the remaining two presidential debates take on even more importance for how this race will continue to play out. Stay tuned.

Maria Cardona is a Democratic strategist, a principal at the Dewey Square Group, a former senior adviser to Hillary Clinton and former communications director for the Democratic National Committee.

John Avlon: Biden overwhelms Ryan

I underestimated Joe Biden.

Before the vice presidential debate, I'd thought that Paul Ryan would have the upper hand -- a young, smart policy wonk and great communicator paired off against an out-of-practice, aging politico with a recurring case of foot-in-mouth disease.

I was wrong.

Joe Biden had clearly studied Barack Obama's failures in the first presidential debate and decided to do the exact opposite -- intensely engaged, smiling and pushing back aggressively at the slightest hint of misstatement or exaggeration.

Paul Ryan was bobbing on the sea of Biden, keeping his head above water much of the time but occasionally overwhelmed by the combined force of personality and facts. He looked like what he was -- an earnest, intelligent, over-coached, comparatively inexperienced chairman of the Budget Committee.