Behavior on a day was driven by factors external to the soldiers' martial fiber. The Yankees at First Bull Run were hampered by bad generalship, lack of training and the task of an untrained force to take a field in the age of rifles. The rebs that day had the easier task of holding their ground. By the time of Chattanooga, the rebs there were handicapped by a bad commanding general and mass weariness and disgust for fighting for an unworthy cause. On that day the American farmers of the Northwest routed their cousins, the American farmers of the Southwest.
I think you have to give it to the South that their boys were more experienced in camping, riding, and shooting—in the beginning. However, war depends on more than the fundamentals (would a nation really good at marching be unbeatable? hardly). What does it profit you to have killed a thousand rabbits as a boy, when you are running toward a column of smoke with thousands of people screaming and dying around you?
Personally, I think the South’s audacity stemmed from the fact that they were in the more desperate situation. They were being invaded, and they lacked the men, the industry, and the “legitimacy” of the Union.