Take I-40, forget US441. 441 has some low clearances, horribly windy and VERY narrow, especially when you go through Great Smokey Mountains NP between Cherokee NC and Gatlinburg TN.
I-40 is good road, there are some steep passes, mostly on the eastern portions before entering TN. There are a couple of tunnels in this section, the clearances posted say you shouldn't have problems but I cruise down the middle of the two lanes using the center of the tunnels...and stay puckered the whole time
It is a beautiful drive...just take it slow and easy!!