This has been hashed over before, but.........IMO, don't take the 421 exit out of Bristol at the hospital, exit 1 or 2, go all the way to I26 Kingsport and go in through Weber City/Gate City. 421 from Bristol to Gate City is curvy and slow especially if you get behind traffic! Just my opinion
The bottom map is a better route in my opinion. But instead of getting back on 421 in bristol and going north of kingsport stay on I81 a little longer until you get to I26. Take it north through kingsport and pick 421 back up near weber/ gate city.