As a rebel commander of a major army I consider only Lee superior to Bragg.
He doesn't have much competition when you think about it.
Beauregard: Didn't command long enough to really evaluate. Creative but flaky and had health issues.
Albert Johnston: in over his head, put bad subordinates in places where they did a lot of harm, lost KY, lost Nashville, bungled the execution of Shiloh, got himself killed in battle.
Joe Johnston: good strategy, bad tactics, never won after Bull Run.
Hood: lost every battle, wrecked his army
Price: mediocre verging on clueless.
Van Dorn: good cavalry commander, but incompetent army commander.
Edmund Kirby Smith: in his only campaign as an army commander he refused to subordinate himself or meaningfully cooperate with Bragg, sealing the Kentucky Campaign in failure.
Pemberton: I don't even need to explain why he's a failure.
If Bragg gets a C to Lee's A then yes he's second-best since everyone else gets a D, F, or Incomplete.
If you count Stonewall Jackson as an army commander from his time in the Shenandoah I'd rank him above Bragg though not by a lot. Stonewall had his only personality issues and was better suited as a corps commander under someone like Lee.
It's remarkable how much Lee stands out in ranking the above. Not just in skill or results, but in the fact that he could play well with others.
Not that Jeff Davis did these guys any favors. He was blindly supportive of some, needlessly combative with others. If we're talking about "temperamentally unsuited" Jeff Davis is a great example.
The Union had its own issues, but laying it out like this I'm starting to see why the Confederates lost.