Cheney appears to have decidedly beaten Edwards.  Edwards just appeared a little bit out of his depth. I think Edwards could have stood up well against Bush, but Cheney just looked like a seasoned pro.

I don't think this will have much affect on the polls though as the veeps just don't make that much of a difference.

I think the key sound bites were very much in Cheney's favor -- i.e. the sound bites that will get repeated will show Cheney hammering Edwards and that is where it could make a difference.