Seniority played a pretty significant role in both armies (although not enough to get McLaws or Harvey Hill a promotion to lieutenant general over A.P. Hill, among other examples).
As for Jackson's seniority:
Not counting Lee, Longstreet, or Cooper, the order is:
Full Generals
Joe Johnston
Beauregard
Bragg
Lieutenant Generals
Kirby-Smith: October 9 (but Major General only since October 11, 1861)
Polk: October 10 (Major General since June 25, 1861)
Hardee: October 10 (Major General since October 7, 1861)
Jackson: October 10 (tied with Hardee)
As for Jackson's seniority:
Not counting Lee, Longstreet, or Cooper, the order is:
Full Generals
Joe Johnston
Beauregard
Bragg
Lieutenant Generals
Kirby-Smith: October 9 (but Major General only since October 11, 1861)
Polk: October 10 (Major General since June 25, 1861)
Hardee: October 10 (Major General since October 7, 1861)
Jackson: October 10 (tied with Hardee)