Battling over their respective economic plans, foreign policy and more, President Obama and Republican Mitt Romney talked over each other and sparred repeatedly during their second debate at Hofstra University, as both sides declared victory.

Snap polls taken after the debate showed a slight edge for the President, though Republicans argued it would not derail the recent momentum for Romney in many polls.

In "Spin Alley" after the debate, both parties did their best to sell their candidate.

"I think the President did a great job," said Sen. Charles Schumer (D-NY).

I hope the third debate is like this one in every way," Schumer added.

A few feet away, it was a different conclusion.

Gov. Romney clearly won it," said Rep. Peter King (R-NY), who acknowledged that the President did better than the first debate, but said Romney was strong as well.

"I don't think it changes the dynamic at all," senior Romney advisory Ed Gillespie said. "This is not about style, this is about substance."

But for the President, part of Tuesday night was about style, as it was a much more animated Mr. Obama than in the first debate two weeks ago in Denver, when the President seemed lethargic and at times disinterested.

"I think the President was great tonight," said senior aide Robert Gibbs, who had a big grin when I asked where was that person back in Denver.

"In Denver, but not as good a participant," Gibbs said with a smile.

One thing that wasn't clear was what kind of reaction there would be to the President's frequent interruptions of Mitt Romney, as well as the bickering that went on between the two men on stage as well at times.

Bottom line on this - both sides declared victory, neither side had a knockout punch, though they certainly had stuff to chew on that the other said.

And they could once again see where they may have missed some opportunities to make a better sales pitch as well.

Tell me who won - and why - and whether this changes the race at all.