Most political observers agree that Romney "won" the debate. I give him only a slight edge after factoring in content, and the degree of truth behind that content. Romney did clearly win the performance contest (aside from that creepy ken doll smirk between responses). He was fully engaged in the moment, and he put Obama on the defensive without looking overly aggressive. He battled. The President simply refused to push back on long debunked claims, and sounded flat and too cerebral.
It needs to be pointed out that much of what Romney said was misleading or vague at best, especially the repeated claim about Obama cutting Medicare. But style often trumps substance in the eyes of the undecided voter. And by that measure it was a big win for the challenger.