Cheney would be one of the most effective TV presences — because of, not despite, his lies — were it not for his irrepressible mean streak. Whether people think he won or lost may well turn on their response to the meanness factor. TV does not like mean.
If you insist on substance, Cheney did almost as good a job as could be done to make the administration look good on foreign policy. Edwards as much as said, 'who you gonna believe: this guy or your eyes?' It's a good argument, but there were others he could have used too. If you were not aware of the facts Cheney was distorting, you might well have thought he won the foreign affairs part, although not by much; if you knew the subtext, then Edwards won on foreign affairs, but didn't do so as effectively as he might have. I think Edwards's stock may rise if people fact check the debate thoroughly, as I think Edwards missed openings to nail Cheney mis-statements.
Conversely, Edwards simply crucified Cheney on domestic issues. Wasn't even close.
Update (10/6): A quickie CBS poll “of 178 uncommitted voters found that 41 percent said Edwards won the debate, versus 28 percent who said Cheney won. Thirty-one percent said it was a tie.” One more time and it's over…..