My compliments Pvt. Saruman, Can't argue w/you about Gen. B. Bragg's capabilities. I think there's a broad consensus that he had his share of failures. I would push-back a little on Pemberton, hwvr. I think he made Grant work pretty darn hard for the Vicksburg victory/surrender.
Since the thread is about Jackson, let's insert him at Vicksburg and Chattanooga. Would Jackson have saved Vicksburg? Not sure what he could have done to save Vicksburg. Once Grant got the "position" on Pemberton, coming in from the south and the east, it was a fait accompli, albeit a "grinder."
Chattanooga was somewhat more fluid, to my way of thinking. Jackson, in place of Bragg, probably would have made a significant influence on the outcome as he favored and excelled at maneuvering in space.
In summary, I believe Grant earned Vicksburg and, to a lesser extent, Chattanooga, whereas Lee & Jackson were handed 2nd. Bull Run, Fredericksburg & Chancellorsville because of obvious blunders by Little Mac, Burnside & Hooker. (I'll subtract Antietam since the outcome was a relative draw.)