Anaxagoras
Banned
Most of the discussion in this thread has focused, quite naturally, on the battlefield commanders. However, I believe that some thought should be given to the "behind the scenes" generals where I believe the Union had a distinct advantage. I believe that generals such as Quartermaster General Montgomery Meigs, U.S. Military Railroad General Herman Haupt and artillery General Henry Hunt contributed significantly to the victory of the Union and were more effective than then their Confederate counterparts.
The Confederacy had an outstanding example of a "behind the scenes" officer in the person of Colonel Josiah Gorgas, the Confederate ordnance chief. He built an entire war industry from scratch had greatly alleviated the Southern disadvantage in military material. On the other hand, their Commissary chief was Lucius Northrop, whose incompetence probably played a bigger role in the food shortages that afflicted Confederate armies than any other cause.
Although this thread is limited to generals, I believe that a brief word should be given to the civilian leadership of the respective armies. Although he may have had a "difficult" personality (some would say repulsive), Edwin Stanton was an effective Secretary of War unlike his several Confederate counterparts.
I don't think there's any doubt that the Union had the advantage here. The South didn't have a decent Secretary of War until John C. Breckinridge took over the department in February of 1865, and then it was obviously too late.