Testy exchanges over topics ranging from the economy to energy to women's rights dominated the second presidential debate between President Barack Obama and former Massachusetts Gov. Mitt Romney, sparking vigorous commentary across the spectrum Tuesday night.

The rematch was a very different occasion from the first debate — a "throw-down," as NBC News' Brian Williams called it.

Here's a selection of the reaction from NBC News analysts and others:

Brian Williams, anchor of 'NBC Nightly News'
"In terms of energy, in terms of body language, in terms of flashes of genuine anger, the kind of DeNiro 'Raging Bull' factor on the floor of this event tonight, it was a vastly different event than any we have seen so far this election cycle.

"In terms of the phrases that may live forever: When Governor Romney said 'binders full of women' when talking about a search for employable Cabinet-level women in the state of Massachusetts. And 'it's just not true' was the president's rejoinder over and over."

David Gregory, moderator, 'Meet the Press'
"I think liberals can breathe a sigh of relief. It's not curtains for the president. He showed up and showed up big tonight. He was more aggressive; he had a lot of fight in him. A little light on his vision for the future, Brian — but no question he made a point of studying his opposition research on Romney. And as you mentioned, over and over again he said, 'What Mr. Romney said, what Governor Romney said just isn't true.'

Truth Squad: The second presidential debate

"Romney was strong, too, wrapping the economic troubles of the last four years around the president's neck. He stumbled on this issue of Libya, saying the president didn't call it an act of terror immediately. That's just not true, according to the transcript.

"A lack of civility in this debate, a lack of control at times, and I think in some cases there were some interesting questions, like the comparison between Romney and Bush, where I think voters would have benefited from a little more interaction, a little more debate in the debate."

Savannah Guthrie, NBC News White House correspondent
"I find it a little bit ironic since this debate was supposed to be all about a fight for female voters, and yet we see these two alpha males at one point circling each other on the stage.

"I think there's no question in watching the performances what the objectives were for each of these respective candidates. President Obama clearly wanted to 're-disqualify' Romney. The Obama campaign had had a good deal of success over the summer and fall portraying Mitt Romney as this uncaring, out-of-touch corporate titan. Clearly, President Obama wanted to get that image back into voters' minds attacking Mitt Romney from the very get-go and never letting up.

Obama, Romney bicker over the debate clock

"And Mitt Romney, on the other hand — his objective was clearly to connect with the ordinary voter. He had a softer tone many times, many times trying to show that empathetic soft side."

Chuck Todd, NBC News political director
"A good lawyer — I would imagine Savannah would agree with this — should know the answer to a question before you ask it. And that's where Mitt Romney, I think, stumbled there at the end on the Libya question.

"Overall, clearly a different President Obama. He came out wanting to make sure he let people know he wants a second term. He was much more engaged. Definitely seemed to study the Romney playbook. He appeared to take Romney as a more serious threat there.

"Romney was rather strong for the first half of the debate. But that Libya moment: You saw the president — you could tell by the way that they seemed to almost practice some of their motions. It was clear the president made the decision when Libya comes up, 'I'm going to stare Romney down right in his face' and vice versa. And that moment is going to be one that's going to be replayed and replayed.

Sharp exchanges between Obama, Romney at second debate

"We could debate whether what was the tone of what the president was inferring when he said 'act of terror' at the time of Libya. But Mitt Romney seemed to stumble, and he seemed to be rattled after that question. He was a different Mitt Romney, I would argue, for the last 15 minutes of that debate.

"Where does this set the race? I think this is one where both bases feel engaged by their guy. I think there's certainly some disappointment in the conservative base that Romney wasn't tougher on Libya. We're headed for a grind-it-out 22 days."

Stephanie Cutter, Obama's deputy campaign manager
"I think the president clearly dominated the debate. The American people saw a strong and decisive leader. That's because he laid out the facts, the facts of his record and where he wants to take this country, detailed plans.

"But he also exposed Mitt Romney for his lack of details on his plans and how his math doesn't add up on his tax plans — how his math doesn't add up on his jobs plan. And I think the more he exposed Mitt Romney on what he was saying in his facts, the more Mitt Romney got combative.

"It was a great debate. It was a great discussion. The president is very pleased. We were able to get out a strong, decisive case for why the president deserves a second term, and we're going to continue to fight for it."

CNBC

Sen. Rob Portman, R-Ohio, Romney's practice debate opponent
"I think he (Obama) was even more annoying than I was at times. The president clearly came out as a different style tonight. We knew he was going to come out swinging, and he did. He telegraphed that he was going to do that. But that doesn't change his record and doesn't change his vision for the future.

PhotoBlog: Watching Americans watching the debate

"And Chuck Todd said earlier he didn't lay out a vision. I agree with that. You can change your style, but that doesn't change the reality that you've got a lousy record. He didn't try to defend it. Then you also haven't laid out for the undecided voter what's going to change in the next four years."

Poll: Who won the second debate?

Andrea Mitchell, NBC News, on oil and gas production clash
"Oil production did fall by 14 percent offshore and onshore, but that was only in one year, from 2010 to 2011, and it was largely the result of fallout from the Deepwater Horizon oil spill in the Gulf of Mexico in 2010.

"Mr. Obama is right. Since he took office, oil production on federal lands is up. Even with the 14 drop last year, overall production on federal lands is still up 10.6 percent since 2008.

"In terms of natural gas production, natural gas production on federal lands is down and has been declining since 2003, according to the Energy Information Administration, mainly because of a decline in offshore natural gas drilling."

CNBC

Jim Nussle, budget director for former President George W. Bush
"I think both candidates appealed to their base. That was job one for both candidates and different than the first debate. I think President Obama performed well in energizing his base.

"The second thing they had to do was appeal to the independent voters — the undecided voters, more especially, the people in the audience asking questions and people at home who still, believe it or not, have not made up their minds. ...

"I think the tenor of this debate is going to turn on the fact that the president still — again, this time for the independent voter, the undecided voter — did not lay out a plan for the future, and I think that's going to set the tone for the rest of this campaign."

CNBC

Keith Boykin: White House aide to former President Bill Clinton
"I think the president ... did a good job of listing what his accomplishments are. He went through the 5.2 million jobs. He went through the 31 consecutive months of private-sector jobs growth. He mentioned the war in Iraq being ended. He mentioned the Osama bin Laden attack. He was successful throughout the night because for every single question, he pivoted and turned it into an attack on Mitt Romney, which is something he completely failed to do in the first debate."

CNBC

Sarah Fagen, senior aide to former President George W. Bush
Romney "gave a devastating critique of Obama's tenure in office, all the things that he did from Obamacare that he thought was bad to Dodd-Frank — and then went on to say all the things he didn't do: immigration reform, Social Security reform, Medicare reform. That was, I thought, Mitt Romney's most effective moment."

LOS CABOS, Mexico -- President Barack Obama expressed support for his European counterparts and their measures to manage the fiscal crisis as the G20 Summit in Los Cabos, Mexico wrapped up Tuesday, saying he believes they are "ready to do what is necessary to hold the Eurozone together."

Behind the scenes, however, one senior administration official said the focus of the summit was to convince German Chancellor Angela Merkel to pull away from an austerity plan and focus more on spending and creating jobs.

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President Barack Obama, German Chancellor Angela Merkel and Chinese President Hu Jintao chat after arriving for the family photo of the G20 summit, at the convention center in Los Cabos, Mexico.

Another senior administration official was asked whether leaders "ganged up" on Merkel; that official replied, "I don’t think I’d describe it that way." But another official said world leaders were very blunt in their efforts to convince Merkel to sign on to the plan.

While the official declaration out of the G20 Summit pointed to a more integrated financial system and an agreement to help Greece stay in the Eurozone, an official says the group was closer to an agreement to create a fund to loan money to troubled countries.

There is no agreement, however, on how such an account would be funded.

Obama said he was "confident" that over the next several weeks, "Europe will paint a picture of where we need to go," but he acknowledged that the world's economy could affect his election prospects. He used the moment to admonish Congress for not acting on the jobs plan he announced last year.

Obama also used his time in Mexico to meet with President Vladimir Putin of Russia and President Hu Jintao of China, where the primary topic of discussion was the unraveling situation in Syria.

While Obama did say he believed both countries understood that civil war was in nobody's interest, it was clear that neither the Russian or Chinese leaders were willing to call for Syrian President Bashar al Assad to step down.

"I wouldn't suggest that at this point, the United States and the rest of the international community are aligned with Russia and China in their positions," the president said carefully.

The president also said he hopes there will be a formal political transition plan in place in Syria in coming weeks, but he was not sure whether Russia or China would sign on. One senior administration official said there was a glimmer of hope that Putin is now willing to consider scenarios where Assad is not in power.