Lets try and cut through some of these misconceptions, yes?

Right after the Civil War, there was something called the myth of the "Lost Cause." It was pioneered by Edward A. Pollard, A Richmond journalist who wrote a history of the war in 1866, called (can you guess?) The Lost Cause. Basically, the book says that the Confederacy was a glorious agrarian state, and was defended by the best armies in American history. Pollard argues that the Armies of the Confederacy were more motivated, they fought better, they were led by better officers, and they were fighting for a noble and glorious cause (the defense of the antebellum south). Many historians, especially in the late 19th and early 20th centuries, repeated this myth and rebuilt it into its modern, "acceptable" form. Basically, they repeated it so often, and so loudly, that the "Lost Cause" became accepted as truth. Men like Douglas Southall Freeman, and even Ken Burns, have been influenced by the "Lost Cause" mythos. More recent historians have moved away from the "Lost Cause" myth, but the myth is still incredibly powerful, especially in conservative and southern circles, where the myth is undergoing yet another reinvention.

So, what of the original question? Were the South's generals really better, or what? Well that depends. As Im sure every other person in this thread will gladly point out, Robert E. Lee was repeatedly able to produce battlefield successes; hes called the American Napoleon for good reason! But he also failed strategically, by wasting the South's precious manpower in offensive battles that cost the Confederacy more than it gained.

And on the other hand, Ulysses Grant maximized the Union's advantage, especially in the Overland Campaign, by using multiple armies to attack the Confederacy all along its border. This strategy prevented the Confederates from reinforcing one area after another, as they had done in 1863, and it also stretched the CSA's manpower to its very limits. So, there, you could say that Grant better adapted his strategy to the unique strengths and weaknesses of the resources at his disposal. In addition, he waged a spectacular series of campaigns, first in Mississippi against Vicksburg, then later against Lee in Northern Virginia, which achieved remarkable battlefield success.

What held Grant back, and what held both the Confederacy and the Union back throughout the war, was the state of professionalism in the wartime armies. Many of the Generals who fought in the American Civil War, on both sides, really werent generals at all. Lee was a Colonel before the war, Grant was a washed up Captain, Winfield Scott Hancock was a quartermaster, Sherman was a Colonel at First Bull Run, etc. Nobody really had the command experience required to maneuver large forces either strategically, or tactically. Unlike in Europe, where generals learnt how to be generals for decades before a war put their training to the test, in America, these men had to learn on the job. What that meant was that those with natural talent, like Lee, Grant, and Sherman, floated to the top, while everyone else made a mockery of warfighting. And when a commander would be wounded, or worse promoted, their subordinates would have to come up to fill the gap, regardless of skill or training. The Armies needed officers, and it was too late to shove a new batch through West-Point to make a general staff.

Thats why we often look at the Union Army, especially the Army of the Potomac under Hooker and Burnside, and snicker. They look so dumb, and these men were give command of an army. But really, I think if you look at what was going on in the Western theatre, and if you look at the Corps commanders of the Army of Northern Virginia, Grant and Lee were the exceptions, not the rule. They were the cream that rose to the top. Even men like Longstreet and "Stonewall" Jackson had major problems with commanding their forces in the field, Longstreet did poorly without Lee's supervision, and Jackson did so with it.

So I think thats the real issue with Generalship in the Civil War. The South was fortunate to have found Lee so early on, while Grant was a gem that had to be dug out of the rough.

If youre interested in reading a book on the topic, I would recommend Russell Weigley's A Great Civil War. Its one of the best books Ive ever read on the Civil War, and trust me Ive read a lot. Plus, Weigley breaks down the strategic and tactical paralysis which plagued the Union, and explains some of the things Ive just talked about far better than I ever could.

I'll just add to what's been said so far that if you look at the north's "better" Generals like Sherman, Sheridan, and Grant, they don't assume theater-level commands until much later in the war, and all three came out of the western theater, which is broadly overlooked. In the popular imagination Gettysburg looms so much larger than the fall of Vicksburg to Grant, a feat which was deemed near-impossible as Vicksburg was the "The Gibraltar of the West."

The Civil War by Ken Burns is an excellent documentary. I would agree that southern generals were better than the north. On some level it is possible that they were naturally better military minds, but I think they also benefitted from the style of war and the objectives that both sides had to achieve to win the war.

The south benefitted from fighting a defensive war. For them to win the war they needed to either get the north to give up or convince European powers to recognize the confederacy and intervene on their behalf. This meant that they fought many battles from fortified positions and did not engage in many offensive campaigns.

In addition, the generals of the south were often times forced to make unconventional and dangerous movements, such as Lees actions at Chancellorsville simply because he was outnumbered and did not have many options. When they worked, Lee was rightfully celebrated as genius.

The north had a more difficult war to win, in my opinion, because they had to convince the south to give up. However, they did benefit from massively outnumbering the south in men and supplies. They also had the difficulty of attacking fortified positions which became extremely deadly during this war due to advances in military technology. The battle of Fredericksburg is a good example do this.

It is worth noting that the southern generals did not perform well when faced with the opposite situation. At the battle of Gettysburg, Lee was in an offensive position while Meade took up a defensive position and the results were a disaster for Lee.

Overall, I would say that the southern generals were more confident and decisive although somewhat out of necessity. The north suffered from weak leaders who were scared to commit men to battle (McClellan) or were overly confident (Hooker).

This topic is very complicated and there are several other factors that contributed to this.

Why were Southern Generals better (or considered better) than Northern Generals in the US Civil War?

Let's consider the major battles on a case by case basis.

Fort Sumter: CSA Victory due to overwhelming force rather than better generals.

First Manassas: CSA Victory due to timely arrival of forces from the Valley per the plans of R.E. Lee (as was the placement of the CSA forces at Manassas).

Peninsula Campaign: CSA Victory due to the flanking strategy of R.E. Lee and the timidity of McClellan (though I never understood why the CSA didn't have better maps of the peninsula prepared before the McClellan amphibious move).

Second Manassas: CSA Victory due to quick marches, deft maneuver, and the inexperience of Pope. Again, R.E. Lee designed the campaign plans.

Fredricksburg: CSA Victory due to superior defensive position chosen by Lee.

Chancellorsville: CSA Victory against long odds due to superior maneuver designed by Lee and Jackson (Hooker's loss of nerve as well).

And the rest is history, and of course all debatable, but I have no problem blaming Lee for the good reputation of Southern Generals.

I highly recommend Robert E. Lee by Douglas Freeman.

The Civil War is an interesting topic because of how different the two "Americas" were, yet how they originated from the same culture.

To understand the difference in generals, you might first have to understand the difference between the United States and Confederate States of America. The North had 2x the railroad track (in miles) than the South and almost all of the Southern steel, iron and other manufactured goods came from the North. There's a famous Southern poem that details how many Northern goods go into making a coffin for a Confederate soldier. So by necessity, the Southern generals had some advantages over Northern generals. In fact, one of the largest population centers in the South was a POW camp for Northern soldiers!

The Civil War was fought largely in the South except for a few key advances/offensives made by some Southern generals into Northern territory in an attempt to capture Washington D.C. or other key Union areas. This lay of the land advantage conferred some advantages to Southern generals (see the prolonged defense of Atlanta by a smaller and worse equipped Confederate force for an example) and Southern generals were also able to use the terrain of the South (in the "Rim South," as some scholars term it, the area is mountainous and rugged, or ill suited for offensive actions) to their advantage.

One of the most famous generals was Thomas "Stonewall" Jackson, who made a career out of not budging out of defensive positions while making audacious and ambitious offenses of his own. He commanded forces at both Battles of Bull Run, Antietam and the Peninsula (Northern Virginia), though at the last he is criticized by historians for relatively poor performance. (See the "Seven Days Battles" for more information.)

Some of his (and this is a strategy shared by the "better" Southern generals that you refer to) tactics included advanced reconnaissance missions (for the time) using cavalry and the use of aggressive flanking techniques to outmaneuver a superior force. The advanced tactics that the Southern generals utilized allowed for a prolonged war in the face of an effective Union naval blockade and lesser supplies. You see here that Southern generals were "better" than Northern generals, but the main point is that they worked with a worse-equipped, smaller force to do damage to a superior enemy.

Sources:

Gavin Wright, Old South, New South: Revolution in the Southern Economy Since the Civil War

Alexander Bevin Lost Victories: The Military Genius of Stonewall Jackson

Gone with the Wind (Just kidding!)

Edit: am I wrongly informed on this?