That would be true to a certain extent of all armies, unfortunately for the much smaller Confederate army, they were stretched pretty thin in those duties.
However the OP I " by what metric is the Confederate Army superior".
Arguably the AnV under Lee was superior to the Union Army in terms of CEVs but the AoP was superior to the AnV in terms of CEVs when it was commanded by Major General McCellen.
So far no indication that soldiers on either side were superior.
Overall both armies were roughly equal in combat proficiency but in the long term the Union Army was a limited manpower superiority ratio did win.