Your link says it! The one you said was the most accurate. But whether it was 12, 15, 24, 29, or 39% can we agree that the prisoners were not treated well? That's all I asked for when this subject was brought up. One bit of honesty. I never said the union treated their prisoners well and I'm sure there were murderers on both sides running the prisons. When I asked if the prisoners at Andersonville were treated well, the answer was "yes", which goes against the thing I asked for...honesty about just one thing.
Overall, including what is known of all the prisons, the death rate appears to be in the 12 to 15% range for both sides
But can you agree they weren't treated well?
There were exceptions on both sides, but the average prison commandant probably did as well as he could. That doesn't mean that the average Joe on either side was treated well or badly. Prison was just a bad and potentially deadly experience for all prisoners.
I think the basic problem was overcrowding on both sides, which was brought about by the Federal decision to stop prisoner exchanges. Prison populations grew slowly until an exchange cartel was reached in 1862, then they fell sharply as prisoners were exchanged. After the North stopped exchanging prisoners in 1863, the prison population boomed. New prisons had to be built, and existing ones had more prisoners than they were designed for. The big death rates occurred after the exchanges were stopped.
Overcrowding lead to rapid spreading of disease among the prisoners. The medicines of the time were probably not good enough to handle some of the diseases that ranged through the prisons, e.g., small pox, etc. Insufficient food didn't help either. Overcrowding also stretched the already limited food supply of the South. A report to the Confederate Congress on the Confederate food situation for the population in general noted that most families of soldiers had not had any meat to eat in six months.
A large part of the Southern population was involved with the war and no longer available for food production. That was listed in the Southern papers as one of the arguments against using slaves in the army. The food supply would have gone to pot.
The fact that there were roughly comparable overall death rates in Northern and Southern prisons suggests to me that there were common factors at work. Disease being the main killer on both sides, I suspect overcrowding with some effect for skimpy and inappropriate food.