At the beginning of the Civil War, both sides suffered from poor-quality leadership in the field.
Assume that you have access to a time machine, and you can move anybody you choose to a different time. For either the Union or the Confederacy, you can take any military leader from any time and place him in command of any army. However, if you choose somebody from after the Civil War, he loses all memory of war history (but not his own experience). This means that he has to rely on his military ability, rather than knowledge of how events played out.
I suspect that either Napoleon or Otto von Bismark would have the best chances of success, partly because they are among the nearest in time – they wouldn’t have to learn as much about the weapons and tactics. George Washington would probably have a reasonable chance; he was fairly flexible. I think that anybody from World War Two or later would have considerable trouble adapting to the difference in technology.
I feel Napoleon is questionable. A lot of the problems in the early years of the war came from generals trying to follow Napoleon’s tactics, which were outdated by fifty years of technological change. Now Napoleon himself might have been able to figure this out and have abandoned his own tactics but I don’t think we can assume that as a given.
As for Bismarck, he was mostly a political leader. It was Moltke who won the battles. He was certainly of the right era; he was fighting wars in Europe at the same time as the American Civil War was being fought. Moltke was a great general and there’s no reason to think he wouldn’t have done well leading American or Confederate forces.
I think one interesting possibility would be if Lee and McClellan had switched places. Each of them seemed to have followed strategies that would have worked better for the other side.
The Confederacy had a substantial material disadvantage throughout the war; it was facing an opponent that had more men and more supplies. But the Confederacy was fighting a defensive war. The overall Confederate strategy should have been to preserve its forces as much as possible and drag out the war until the United States gave up. The Confederacy couldn’t beat the Americans but they could make them quit.
Lee saw it otherwise. He tried to force a victory by beating the Americans in battles. His strategy was that if the United States lost enough battles it would give up. But he didn’t see the effect of the material disparity between the two sides. The Confederates were suffering more from the battles they won than the Americans were suffering from the battles they lost. A string of Confederate victories would defeat the Confederacy before it would defeat the United States.
McClellan, on the other hand, was a general who couldn’t face a battle. Time and again, he maneuvered his army into position and then couldn’t give the final orders. He was too afraid of losing to commit to a battle.
If the two men had switched places, Lee would have been seeking battles but with a material advantage. Winning battles would have advanced the American cause in a way it didn’t help the Confederates. And McClellan’s unwillingness to fight battles would have helped preserve the limited resources of the Confederate army.
I’d take Stonewall Jackson and place him in command of 3 random Pushtans in the mid-1500s. That way Lee is deprived of his “strong right arm” from the very beginning and the South loses all the quicker. Or I take the Grant of two days before the end of the war and move him back 4 years and place him in over-all command of Union forces. That way he knows what works and what doesn’t, what the South is going to try and when, and can crush them mercilessly.
Quite honestly, your best best is to make Ulysses S. Grant in charge of Union armies from the get-go, with Sherman and Thomas as his army generals. Grant was the best general in the history of the United States.
Grant would do a far, far better job than would Napoleon, who would have not fully understood the physical and technological nature the way Grant would have - Grant was, as John Keegan described him, “the first modern general,” and in the grand American tradition understood that professionals discuss logistics. Keegan wrote that you could have kidnapped Grant and stuck him command of an American army in World War II and he’d have things figured out in a matter of weeks; I happen to agree that’s true.
But if you send back a modern general, they’d struggle with the politics of the time. The U.S. army in 1861-1865 was politicized to an extent inconceivable to us today; today’s American armed services is a completely professional and authoritarian organization. The army of 1861 was egalitarian and political to an incredible degree; officers were elected colonel of their regiments, generals appointed based on regional representation and political connections, and it was difficult to keep soldiers from running away if they decided they didn’t like serving. Grant, a man of that time, understood how to deal with that stuff to an extent Patton or James Mattis or whomever wouldn’t. Today’s general would find it baffling why he had to keep an idiot in charge of a whole division because of political pressure from some ass in Wisconsin.