I'm using Nero 6, so if you're using a different version things may differ a little. First, can you burn a dvd with the destination drive using the dvd-r discs you want to use - I mean, not to copy, but just to burn anything. Because that would rule out the problem being the discs - and I still think it's not the discs. I've only heard of that message if you were trying to copy a dvd to a cd or a double layer dvd to a single layer - something like that that would be physically impossible for the program to do without using a special setting.
In Nero 6 you want to choose Copy and Backup, copy entire disc, you want to make sure that you tell the program you are using dvd's and not cd's, if both drives are burners you can play around with using which one is the reader and which one is the burner. It should be pretty straightforward. I would again suggest dropping the writing speed of the burn drive. Also, the drop down menu that gives you a choice of burn drive also gives you a choice to burn an image. I think you should test that. Burn an image, then use Nero to burn the image to dvd. That should avoid any configuration problem. There are other programs besides Nero you might want to consider is you decide to use that method (ImgBurn) but I'd test it with Nero.
The other alternative is to choose Copy An Entire DVD movie. This rips the movie to the hard drive, and then you can burn it again onto another dvd.
I have used the Copy Entire Disc function without a problem, so I know it works. But if you can't get the settings right try one of the alternatives