Hood was an excellent brigade commander, then division commander, until the first phase of his career in the civil war ended with his wounding at Gettysburg. When his men were sent to Chickamauga he joined them despite not being fully recovered, and was seriously wounded again at Chickamauga. The leadership vacume and confusion created by his wounding seriously impacted Hood's attack and prevented them from pushing the Union troops off the field.
But after that, he had serioius problems. He was not well suited for corps and army command. He complained to Davis about Johnston, causing Johnston's removal just outside the defenses of Atlanta, and his own appointment there. His attack (the next day?) had a solid plan if the odds had been even, but was overcome by the greater numuber of Union troops and their ability to put artillary into action on short notice. As it was he set the stage for the the AoT for the rest of the war: throwing itself at superior union forces and taking huge losses it couldn't afford to take.
At Franklin, he didn't really force the Union forces across the river, they wanted to join Thomas in Nashville. Hood hoped to cut them off, defeating a comparitively smaller portion of the Union forces in detail. The attack ended up throwing the creme of the remaining AoT against cannon and entrenchments at Franklin, losing the best in the process (Cleborne, etc.). A better commander would have looked harder for other flanking options, Forrest thought he found a good way to cross and get behind the enemy.
And what did he really expect to accomplish against Nashville? It's defenses were so solid that even Bragg never dreamed of pounding his army against them. He didn't have enough men to beseige it, they could only sit outside one portion of the city while trains brought reinforcements several times a day in from elsewhere. His men fought bravely at Nashville but were essentially outnumbered and outflanked by Union cavalry fighting dismounted with repeating rifles.
After Nashville, the AoT was so effectively destroyed as a fighting force that it was dismembered and it's various parts sent elsewhee (Mobile, N. Carolina, etc.). At that time it was estimated that one-third of the remnant was so sick, wounded, or crippled that they were unable to serve further, so those were simply sent home.