IMO Jackson was one of the better commanders on either side during the war, but as noted above was by no means perfect. I've given thought to some categories where a good commander needs to excel and provided my assessment of Jackson's strengths and weaknesses. I have to think that Jackson's reputation benefitted by his dying before the War turned against the South. Whether events would have differed had he lived is for 'What if' posts. For the most part I did not mention the Seven Days. The reason for Jackson's poor performance, whether physical, psychological or whatever is unlikely to ever be known for sure, but IMO does not add much information as to how he operated.
Operations
When it comes to strategic plans and movements I find few better. Jackson had a good eye for terrain and when given the opportunity selected his ground well whether on offense or defense. He excelled at moving his men quickly to take advantage of strategic opportunities left open by Union commanders. He was a proponent of the expressions "Hit Em Where They Ain't" and "Get There First with the Most Men" before those expressions were invented. Despite his reputation as an aggressive commander, Jackson could temper that aggression. At Sharpsburg and Fredericksburg it seemed that opportunities for counterattacks were present. Jackson took the time to investigate further, but backed off when he realized the odds against the Confederates. That was not always the case as Jackson did attack headlong into unfavorable situations at Kernstown and Chantilly.
Tactical abilities are IMO more open to debate. Jackson's disposition of the troops under his command was less than stellar at Kernstown, Port Republic and Cedar Mountain. Jackson's troops were fed into battle piecemeal and somewhat disorganized at Gaines Mill, but that is probably due to the exigencies of that battle. Tactical arrangements at 2nd Manassas and Fredericksburg caused problems during those battles, but I think much of those issues can be attributed to the subordinates responsible for those arrangements. It seems to have been a common occurrence in the Civil War for a commander to give orders and leave the implementation to the subordinate. Commanders on both sides (e.g.: Lee in the Seven Days, Bristoe Station, along the North Anna and many would say Gettysburg, Bragg at Chickamauga, Hooker at Chancellorsville, Meade at Gettysburg) frequently had to deal with such problems as that command style caused.
Logistics
Jackson seems to have developed a very capable staff. I find little evidence of his men lacking basic supplies necessary to carry out their duties whether obtained from Confederate or captured Union sources. His successors in command of the Second Corps retained his staff in their positions following Jackson's death.
Intelligence
A mixed bag in my mind. Jackson seems to have been very keen on obtaining information concerning the area in which he was fighting and dispositions of his opponents. Jedidiah Hotchkiss maps were drawn at the behest of Jackson. His ability to find weak spots in Federal dispositions was well demonstrated in the Northern Virginia Campaign and at Chancellorsville. Jackson knew the value of cavalry in scouting and screening and his ability to cooperate and coordinate with Jeb Stuart has been noted. Stuart, however, was under the command of Lee who dictated many of the moves. Jackson's ability to command his own cavalry under Ashby and Steuart was not so good, but neither were Ashby or Steuart. Jackson seemed to be able to adapt quickly to changing situations and move his men quickly in response.
While Jackson did communicate and coordinate well with Lee, Longstreet and Stuart, his near paranoia concerning his own plans and keeping them from subordinates was legendary. He frequently quoted Frederick the Great in saying "If I thought my coat knew my plans, I would take it off and burn it." This penchant for secrecy came back to bite him on a number of occasions. At Kernstown BG Richard Garnett ordered a retreat when his troops ran out of ammunition. He didn't know Jackson's plans and couldn't find him. The fatal wounding of BG Charles Winder at Cedar Mountain found his successor, BG William Taliaferro, totally ignorant of Jackson's battle plans just as Banks' Federals began their attack on the Confederate left and probably contributed significantly to the difficulties of that battle.
Personnel
Stonewall's difficulties with his subordinates were legendary. Most prominently A. P. Hill, William Loring, Richard Garnett, Charles Winder and Maxcy Gregg were among the more prominent names that ran afoul of Jackson's ideas on discipline. Hill found himself under arrest for not having his men take prescribed rest breaks. Jubal Early was about to be chastised when Jackson him why he (Jackson) saw so many stragglers behind his command. Early had the gumption to respond that Jackson had seen so many stragglers because he rode behind the division and so escaped unscathed.
More than a few capable and talented Confederate officers resigned as Jackson promoted favorite subordinates over their heads. They didn't meet Jackson's ideals concerning discipline and morality. Jackson was not above using character assassination in undermining the reputations of those he did not approve. Initially the private soldiers of Jackson's command grumbled a good bit about discipline, forced marches and unpopular officers place over them. Eventually success overcame their doubts.