"On the army level, though, I would disagree. Yes, they had Robert E. Lee, the best general of the war, but they also had walking disasters like Pemberton, Bragg, and Hood placed in command of their armies."
One thing I should have pointed out was that since the Confederate Army was smaller, they had fewer senior positions to fill and there was less of a chance for duds to sneak in.
I also agree that the Confederate advantage in leadership was more at the brigade/ division level than at the army level, and more in the early than the later years.
However, look at the army commanders on both sides (Pemberton by the way was never more than a corps commander):
1862
USA: McClellan, Burnside (replaced McClellan), Grant, Buell, Halleck (department, later CinC), Butler (department,but one corps), Pope
CSA: JE Johnston, Lee (replaced JE Johnston), AS Johnston, Beauregard (replaced AS Johnston), Bragg (replaced Beauregard), Holmes (departmental, not many troops)
1863
USA: Halleck (CinC), Hooker, Meade (replaced Hooker), Grant, Rosecrans, Thomas (replaced Rosecrans), Banks, Sherman
CSA: Lee, Bragg, Kirby Smith (departmental)
1864-5:
USA: Grant (Cinc), Halleck (deputy to Grant), Sherman (deputy to Grant), Meade, Thomas, McPherson, Howard (replaced McPherson), Banks, Hurlbut (replaced Banks), Butler, Ord (replaced Butler), Slocum
CSA: Lee, JE Johnston, Hood, Kirby Smith (departmental), Beauregard
What jumps out is the greater number of USA army commanders compared to the CSA ones.
This represents the much larger size of the USA army, there were simply more armies to command. But it is also due to greater churn. They had to go through alot of generals before they got heir successful 1864-5 team in place.
Dandan Noodles makes another excellent point, the USA army as it existed in 1861 was simply not designed to fight a continental war against an large army. But then the CSA army didn't exist at all. I really think the Confederates just were able to ramp up more quickly, but as long as the Union kept at it they were going to catch up.