I didn't think either of them was a clear winner, 'cause they both danced around questions and avoided direct answers in an almost comical fashion. wbam mentioned how Edwards did it, there was also a point where Cheney took himself on a tangent about education, and when it was Edwards' time for rebuttal, he was like "...the question was about jobs and poverty, right?"
If I had to pick a winner, though, it would have been Cheney, which is why the instant pollings following the debate surprised me(even 120,000 Fox News viewers gave it to Edwards, 53%-46%, with 1% actually taking the time to log on and vote "I was watching baseball"). Cheney got in more effective digs, especially early on before it looked like he was about to nod off near the end.
I was told by someone that Edwards could've torn Cheney a new one when he was bragging about the '84 El Salvador elections, but I guess Edwards didn't read up on that situation. I don't know anything about it, either, so I wouldn't know...