I grew up several decades ago in the Cumberland Gap area of Tennessee so I have a rough idea of your weather. You can get a few days unsuitable for man or beast to go outside but your chickens should be able to get outside most days.
Both coops have about 16 square feet of space inside. That is really tight for 6 hens. Both are raised. The
TSC one has the bottom enclosed so it is wind-protected. The
Wayfair one is mobile but open, so not much wind protection. Maybe you could box it in?
The big run is covered in 1/2" hardware cloth so pretty well predator protected. I can't tell how big the openings are with the
TSC run. There appear to be gaps between the supports. It should stop any bigger predator but mice, rats, snakes, and weasels could probably
get through. Even of you put hardware cloth around the bottom they could still climb up and get in above it.
With both runs many critters could push their way under the bottom supports. Would not take much digging, if any, if your ground is not perfectly level. I'd put no-dig protection around either one. Attach wire mesh 12" to 18" wide around all sides to the bottom and lay them out horizontally. Bury them about 2", just under the turf to hold it down out of the way of lawn mowers and weed eaters.
Neither one are very proud of the insides. I could not find photos to see that much detail of how they are laid out inside.
You can attach shade cloth to either to provide shade. Or use tarps.
My preference would be to have a bigger coop section for either of them. To me that is the biggest drawback. If you make the run predator proof you could always leave the pop door open so one can get away if they get violent because they are so tight.
I know you are looking for prefab, you do not want to build it yourself. I'd look for a bigger coop if you can find one and maybe look at a 10 x 10 covered dog kennel. Expanded metal or chain link. Or get that large chicken run. It should work with a coop inside.