Right now, I am doing the very drive you are planning, I have just come off Skyline.... drove the first 65 miles and then reverted back to I-81. Like the BRP, Skyline is slow, but very scenic, and if you like to stop at the turnouts for photos and admire the view, then that makes it slower still.
For me today it was fog and rain... and then rain and fog... very little to see and enjoy. This is the third time I have attempted the Skyline / BRP, and each time I have been thwarthed by the weather. As I drove down I-81, I kept listening to the weather on the radio, and looking across to the mountains. The clouds were very low, shrouding the tops of the mountains. I doubt that I would have had much scenery to enjoy.
On the other hand... a wild turkey crossed my path - got a good photo - and many deer were by the roadside, including some young ones.
Lifey in Roanoke