I wanted to start with the one person I thought would probably be most universally chosen. I honestly think that most people are going to think of Lee as the epitome of America's greatest military foe, for a number of reasons. Let me outline them below.
First, Lee is a romantic figure in American history. We associate him with being a gentleman and a general. He becomes a reluctant warrior for the Confederacy because he could not forsake his home; his commitment to the Cause was perhaps not as strong as others. None of that would have mattered though, if he could not marshal his troops well on the field.
On the attack, his Army of Northern Virginia pushed the Army of the Potomac back; he forced Lincoln to change his commanders until he found ones with the skill and mettle to meet Lee in the field. He managed to turn what looked to be a decisive Union advantage in men and war materiel into a long, drawn out and bloody conflict. While both assaults into Union territory were pushed back, it is probably amazing that one, let alone two, were possible given the South's position. I see the choice to assail Gettysburg described as a blunder; there is no doubt though, in my mind, had Lee been successful, his gambit would have succeeded. The longer the campaign went, the worse it was becoming for the Confederacy, something that Lee, Lincoln and Davis all knew. Gettysburg was a failure, but there was no better commander available for the Confederacy.
Lee didn't only show his chops on the offensive; if I remember, he was slammed by Confederate media for his early defensive postures. Preparations that perhaps saved Richmond when it was assaulted and ended the Peninsula Campaign with a favorable result for the Confederacy. The Army of Northern Virginia saved Richmond and won battles despite being outnumbered and out gunned. Lee held the line in multiple battles, turning what could have been routs into bloody, almost Pyrrhic victories for the North.Though he was ultimately defeated, Lee's military acumen was praised in the North and South.
Not only do we have to take into account his military skills, we have to look at what these enemy commanders were able to bring to bear against America. Lee's army was much smaller; though its logistics lines were often shorter, they did not have the advantage of railroads to move troops and supplies, and his politicians were more frequently hobbling him (such as sabotaging a much hoped for alliance with France or Britain against the Union). While the politicians trusted Lee, their actions were detrimental to his goals.
Where he lacked the ideal situation above him, his subordinates were superior commanders. Stonewall Jackson is probably the most famous; as we move further into the past, excellent subordinates and lieutenants are significantly more valuable assets, especially in larger areas of operations and harder communications.
Lee's desire for a unified America eventually reasserted itself after he was vanquished. He accepted defeat like a gentleman and was probably instrumental in preventing the Klan and the South from devolving into even greater rebellion after the war.
Now, he was within striking distance of the heart of America, and had he even fought to a draw, the U.S. as we know it would not exist. He may not have even needed a draw, a bloodier loss than he had, or even just a loss that dragged out a few more months, may have permanently reshaped the Union. I haven't written or posted the other general overviews, so we can't really compare them yet, but I think, after this brief recap of Lee's career, I feel confident in putting him as one of the five commanders I would select for the finalists as America's greatest military foe.
These are going to be fairly basic level readings, and I'm shooting a lot from memory, so I hope not to make too many (if any) errors. My sources for this are my memory, a Civil War atlas I have and Encyclopedia Virginia. Where I needed memory refreshers, I trusted to Google and Wikipedia, which I would never do were I trying to be scholarly. But, this is kind off the hip. Were I to retool these essays for some sort of publication, I'd be much more thorough and make fewer assertions. The best citation I have for the atlas is (in a terrible, horribly butchered citation, because I have the Amazon link):
Maj. George B. Davis, "The Official Military Atlas of the Civil War," (U.S. Army, 2003 ed.)