If you have enough light the 70-300VR will focus a bit faster, but you need a lot of light to stop action or shoot at higher ISO with its smaller maximum aperture.
The 80-200 is still selling well on ebay for used. They are fetching around $650 or more. The 70-300VR can be had for $409-459 brand new. I paid less and got a nice lightly used one.
I echo the above sentiments.
I've used both lenses, and while the 70-300 VR is a great lens, the optical quality of the 80-200 is far superior. You can get a used two ring version for a (relatively) reasonable price.