Natchez Trace starts out in the hills in TN and then gets flat as you get into AL. Slow speed, restricted access, nice ride when you have nothing better to do. Lot of interesting history.
BRP is in the mountains with some good views and curves. The two parkways are totally different.
If you want to see local culture, pick any wiggly road that crosses the BRP. You will still have the mountains, views, and curves. Often the road will not be as well maintained but you will pass through a few small towns.
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