Both routes have their advantages and fans. You really can't choose one until the day before you depart and check the weather. If a snowstorm recently passed the area, what are the road conditions? If a snowstorm is approaching, traveling farther to the east may give you a few extra hours of dry roads.
Know the conditions in the mountains between Nashville and Chattanooga on I-24. If they're icy or fog is expected, you may need to take the I-65 route through Alabama rather than risking the I-24 to I-75 routing.
Christmas Day we drove from Chicago to Orlando and my planned route took me via I-57 to I-24 and Nashville. That was the day the winter storm was headed across the deep south. It had cleared the western portion of the deep south but was hitting Nashville, Birmingham and Atlanta on that Saturday. So I rerouted us on a western routing via Memphis, spending the night there instead of Atlanta. It allowed us to go around the winter storm. It was longer overall but at least we did not hit the icy roads that existed further east.
BobK/Orlando