Yes and no; in all cases, the decisions the combat commanders made
As far as Gettysburg, those are just decisions of the leaders. It arguably wasn't in his nature, but Lee could have decided that the Union position was just too strong and done what Longstreet suggested -- entrench on good ground between the main US force and DC. If he'd done that, Meade might have felt he had little choice but to attack. Even aside from Lee and Meade, numerous subordinate decisions could have affected things -- CSA corps moving faster or slower, US corps likewise, more US forces doing their own thing (Sykes) with disastrous results.
Vicksburg is similar. Grant might have maneuvered less effectively and his opponents more effectively. Johnston and Pemberton could have worked MUCH better together, Grant could have done a bloody assault before the US had a strong advantage etc. At the least, the fall could have been delayed months.
As far as leader, keep in mind how long it took the US to get to those and some of those are somewhat debatable. Also, I think the CSA might reasonably count at last Johnson and Jackson.
Yes and no; in all cases, the decisions the combat commanders made reflect their experience in the previous years of the war; Lee's overconfidence, for example, or Meade's caution. Likewise, Grant's determination vs. Pemberton's hesitancy and JE Johnston's vacillation.
The command organizations also reflect the lessons each army had drawn; in the West for the Vicksburg campaign, there was one supreme commander - Grant - for the US, who had - literally - more than two years of experience at every-increasing levels of responsibility, including working directly with his principal subordinate, and excellent cooperation with the Navy, and with a very capable staff that had developed and improved since Belmont. Likewise, Grant's forces were concentrated, well led at the corps and divisional level, and had excellent communications.
The rebels were separated under Pemberton and Johnston, neither of whom had the solid and uninterrupted service that Grant had, poor staffs and subordinates, and lousy communications - much less anything approximating a navy.
The same essentially holds true for Meade and the Army of the Potomac in comparison to Lee and the Army of Northern Virginia.
As far as the 6 sucessful army commanders to 1 reference, the reality is all six of those listed did not lose a battle at the army level or above to their rebel counterparts; Jackson lost at Kernstown to NP Banks, and never held an independent command after the Valley; and it's unclear which Johnston you are referring to, but AS Johnston lost the only battle he led, and JE Johnston, although fairly capable on the defensive, also lost the only significant army-level offensive he tried to command (Seven Pines).
Even Lee, despite his undeniable brilliance, had his share of failures, on the offensive (Seven Days in the grand tactics sense, and both Antietam and Gettysburg period) and the defensive (West Virginia, Spotsylvania, and the Wilderness, ending with Petersburg and Appomattox.)
Grant never lost a battle, essentially, and certainly never lost a campaign; and the other five - Sherman, Meade, Thomas, Sheridan, and Ord - were all sucessful and (notably) still alive, effective, and in the field at the end of the war. Jackson, of course, was dead, as was AS Johnston.
The rebels really don't compare, in any way, and the huge population differential in favor of the US was reflected across the board in terms of the US war effort, from battlefield commanders to administrative experts to political leaders.
Best,