I voted for Bragg. Really, you'd think the man could get at least some credit for his leadership of the Army of Tennessee. After all, he's the guy whose campaigns convinced Kentucky to join the Confederacy, enabling Lee to use that state as a staging ground for his famous attack through Ohio and on to Cleveland that cut the Union in half and enabled Lee to go for the kill. Bragg also did a very good job of overcoming the defense of Chicago, and that's a feat no one can deny.
(OT: I'm not entirely sure that Robert E. Lee would ever abandon Virginia to launch a raid across Ohio. He was always far too concerned with how Virginia would be effected by his decisions to ever do such a thing and really doing something so reckless would leave Virginia far too exposed to a Union counterattack and leave Richmond almost defenseless to that counterattack, so I'm going to substitute Robert E. Lee for Stephan D. Lee and go into it here.)
I am of the opinion that Chicago made Bragg untouchable by history. If he hadn't died at the moment of his greatest success then he would have been more open to criticism by the post-war commentators of the conflict.
The Third Battle of Chicago (as it should be more accurately named) was fought not because it was something Bragg wanted to do but something he had to do.
He had launched the invasion of Indiana with the singular intent of reaching the Great Lakes and taking the fight to the very heartland of the Union. He did this without taking proper care in whether or not his supply lines would be protected.
Bragg's plan was to use his Army of Tennessee (a force of around 60,000) to attack through Indiana and reach the Great Lakes while leaving Stephan D. Lee's Army of Kentucky (a force of around 30,000) to keep William Rosecrans Army of the Cumberland (a force of around 60,000) busy.
Bragg managed to slip past Rosecrans and get to Batesville, Indiana before Rosecrans even knew he was gone. Rosecrans set out to follow him but was soon blocked by S.D. Lee's Army of Kentucky and forced to withdraw following the Battle of Braysville.
Rosecrans worried about losing his job if he let Bragg go unhindered into the Northern States but he needn't have worried because his superior in the Area, Henry Halleck, informed him that he had brought John Pope back from fighting the Indians to lead a new Army against Bragg and told Rosecrans to focus on Kentucky.
Rosecrans however did take one more move against Bragg. He deployed around 18,000 men under the command of Philip Sheridan to harass and strangle Bragg's supply lines. The small Army of Kentucky would be too hard pressed with Rosecrans to to actually make any real difference in protecting the supply lines
S.D. Lee realized that he wouldn't be able to protect Bragg's supply line and fight Rosecrans at the same time and, because his orders from Bragg were only to focus on Rosecrans, he ignored Sheridan and focused on Rosecrans.
Bragg had the opportunity to deploy any one of his three Corps (Hardee's D.H. Hills of Polk's Corps) to attack Sheridan and have a good chance of destroying his force at Hamburg before he got too far into his Indiana campaign but chose not to.
That decision was one of the worst he ever made.
After a series of running battles with Pope's Army of Idiana across that state (Pope tending to withdraw when Bragg go the upper hand, having been taught a harsh lessen in Virginia about being too offensive and letting himself be flanked) Bragg was involved in three Bloody assaults on on Chicago, the first of which he won but was unable to take the city, the second he lost but was not force to withdraw and the final one he won and took the City.
The whole reason Bragg chose to attack Chicago in the first place was because Sheridan had stopped all supplies reaching him and he believed that he could get fresh supplies from Chicago. Though Bragg's final assault of the City left the Army of Tennesse in charge of it Bragg himself fell in the attempt to a lucky shot to his left brest and Hardee, who took temporary charge of the Army of Tennessee following Bragg's death, found the supply depots in the City too strongly defended to get anything from.
The Army of Tennessee was soon forced to withdraw right back to Kentucky, masterfully handled by Hardee, and the whole campaign was a failure but because Bragg managed to gain control, for a short time, over Chicago and before he died the Army of Tennessee were perceived to be in a very strong position Bragg faced no criticism for his poor decisions.
President Jefferson Davis said that the loss of Bragg was the biggest tragedy the Confederate states had suffered since the death fo A.S. Johnston.
But, even though Bragg fell, the west was to see another great commander emerge when S.D. Lee took the fight to Ohio.
S.D. Lee's Ohio Campaign saw him easily outmaneuver Rosecrans and gain easy access to any part of that state he wished. Rosecrans did a very good job of chasing S.D. Lee and bring him to battle when he needed to but S.D. Lee always somehow managed to escape with his army intact and continue to threaten Ohio.
It was largely through S.D. Lee's work with the Army of Kentucky in Ohio that allowed the Army of Tennessee to regain itself after the failure of the Indiana campaign and become an effective force in the theatre again. They would never again launch an invasion like Bragg's Indiana or Kentucky campaigns but they did, nevertheless, keep the enemy at bay long enough for the war to be won.
The fact that Stephan D. Lee's invasion of Ohio was much more successful than Bragg's invasion of Indiana or that S.D. Lee took Cleveland with far less casualties than Bragg took Chicago is often overlooked by general history just because the fall of Chicago coinciding with the death of Bragg is so much more romantic in imagery.
S.D. Lee isn't as high profile as Bragg was either so he does tend to get overlooked.