Here are the details of each route:
I-65:
* Distance: 310 miles
* Time: 4 hours and 40 minutes
* Route: Take I-65 South from Louisville to Elizabethtown. Then, take KY-61 South to Glasgow. Finally, take TN-297 West to Gatlinburg.
I-75:
* Distance: 375 miles
* Time: 5 hours and 35 minutes
* Route: Take I-75 South from Louisville to Knoxville. Then, take US-441 South to Gatlinburg.
As you can see, I-65 is both shorter in distance and takes less time to travel than I-75. Therefore, I-65 is the faster route to go from Louisville, KY to Gatlinburg, TN.