Only been to Cheatham once, what I remember is it was hilly. Close to Nashville and pretty country.
LBL is beautiful too, but something like 60,000 acres in TN, so narrowing down a spot will be tough. Most campgrounds at LBL might be closed in Dec, but you could primitive camp. You also have to purchase a permit for LBL, assuming you have a Sportsmans License and no additional tag for Cheatham. LBL is prob 1.5 hours further away than Cheatham for you as well.
Both are big woods type of hunting, pressure will be lower at LBL but finding a food source will be your issue there. Same as Cheatham I suppose too.
Honestly its a flip of a coin, I would choose LBL only because I know the area better than Cheatham and you would have it to yourself.