I think I have read in your other posts that you must work in your new location, so I think the determining factor might be which area offers the highest concentration of jobs. Working to pass the time or "busy oneself" in retirement is one thing, but needing to work and be a part of the regular work force (health insurance, pension, annual leave, sick leave, etc.) is something different. Can you try and find out which area has the highest concentration of jobs in your field - KY or TN?
It can be such a catch-22 situation with some places that have a low cost of living - they either don't have a high concentration of jobs or the hourly wage is not as high as the larger cities.
Maybe doing a search using the word "employment" in the Knoxville and Chattanooga forums as well as the KY forum will give you threads where employment or the lack thereof is being discussed.
Hope this helps! Good luck.