The nub of the rail power issue - essentially all you need to say about it in comparing North with South - adds up to two facts buried deep in George Edgar Turner's Victory Rode the Rails.
He observes, in Chapter 18, that in the early war the Confederate legislature rejected a bill to allow government control over the railroads where in the Union such a measure passed. Much of the book can be read as an elaboration on those two events.
As for the rest, Turner does a very interesting thing, rather like what Rowena Reed did in her book Combined Operations in the Civil War. He takes this aspect of operations that he is interested in and converts it into a paradigm by which he evaluates the various commanders and campaigns.
Consider the general campaign narrative that takes no notice of railways, except where track is broken or some junction made an objective; take the next step up, the analytic histories of Hattaway or Jones, where single lines are evaluated in terms of their carrying capacity to supply an army.
Turner goes beyond this in significant ways. He
(1) Analyzes the total rail potential of a given tactical position. So, "Thus was formed a parallelogram, three sides of which were first class railroads and the fourth the army's new defensive line."
(2) Determines whether the commander on the ground understood the rail potential of his position.
(3) Looks at the effects on rail power of tactical and movement decisions taken by footborne commanders making positional decisions. Here Johnston gave up a rail-reinforceable position; there Jackson forestalled an advance near Staunton's junction.
(4) Evaluates rail lines in terms of their individual physical potential to deliver troops as well as supplies.
(5) Looks at the unintended consequences of rail use. So, Johnston's rail-based troop concentration at Corinth demonstrated Corinth's importance and may have made it a target.
Needless to say, this is the kind of treatment that makes foolish many hoof and foot campaign histories (Reed did the same in her field). At the same time, it is only a first attempt and unevenly applied. Most problematic is the question of what a particular commander knew or understood.
Nonetheless, Turner's rich paradigm has long been available to Civil War storytellers; pity they have shelved railpower analysis with so much other analysis.