Lee was a great commander at the tactical level, he knew how to win battles, and he usually won them while being outnumbered. He deserves praise for that. Where he was lacking was at the strategic level; he could not piece together a war winning strategy. As was said to Hannibal; "You know how to win battles but not how to use them."
Eh, Lee was only as good as his corps commanders. Once he lost Jackson, his string of victories ended. He still had the excellent Longstreet, but he didn't listen to him. Lee is highly overrated and coasted on the aptitude of his subordinates.
@Snake: I don't think you can really compare Falkenhayn and Lee except superficially. Both of their strategic imperatives were different. Falkenhayn knew that time was against him, i.e. waiting would mean the Entente would use its manpower and material to bury Germany and they would bankrupt themselves to do so.
Lee just had to wait out the Union, but instead wanted to try and force a quick end to the war through maneuver despite lacking the logistics and manpower to invade the north. He let himself get sucked into the battle that the Union wanted to fight and lost his best troops in an ill-conceived invasion that would under no circumstance have won him the war. The Union had a limit to the losses it would take and the length of a war it would put up with; the Entente did not thanks to trade with the US and European concept of total war. The US Civil War was a fight to exhaustion; the Great War was a fight of annihilation.
The problem with Falkenhayn was that he won no spectacular victories ala Tannenberg that would give him the credibility to continue with his attrition strategy long term.
Uh, Gorlice-Tarnow and the Eastern Front campaign in 1915?! He inflicted over 1 million casualties on the Russians and saved AH from defeat. He also had the Serbian campaign under his belt and the defensive victories of 1915. These were all far more important that the victories of Hindenburg and Ludendorff; Tannenberg wasn't a H-L victory either: it was designed by Prittwitz and his staff (including Hoffmann) before H-L showed up. They just approved it and took all the credit after it was already in motion. There is a reason that Hoffmann went around telling people about where Hindenburg slept before, after, and during the battle.
Let's not forget the unpublicized losses of Ludendorff. The 2nd battle of Lodz in January 1915 cost Germany 100k+ casualties for no gain; their cavalry maneuver during the 1915 campaign was smashed at Minsk with the loss of most of the force, just as Falkenhayn predicted; also the 2nd Masurian campaign was far less successful than portrayed in the German media at the time. H-L's reputation was based on propaganda, pure and simple.
The problem was that Falkenhayn told the politicians that the war was unwinnable in 1914 and 1915 and that they needed to make peace; H-L told Bethman-Hollweg that they could win the war, despite having little understanding of the situation outside of Prussia, which Bethmann stupidly believed. In fact he was so willing to believe them because a victory was the only way he could save his job, which was far more important to him than saving Germany! Of course there is much more to the story that just this, but it all hinged on politics. H-L were willing to meddle in politics to achieve their ambitions, while Falkenhayn still respected civilian institutions and focused only on military matters. Falkehayn was brought down by politics, not his battlefield conduct. He just wasn't prepared for the dirty games of the terrible two.
Remember that following Cold Harbor people in the North were calling Grant a butcher and felt his campaign had accomplished nothing. They focused on their own losses and did not have a rational detached view that it didn't matter how much they suffered so long as the South suffered even more. It was only the capture of Atlanta that restored public confidence. Prior to that Lincoln expected to be defeated in the 1864 election.
By then the South was already beaten. It just took some time to bring the Confederates to heel. The US public was unaware of what was really going on.
If the Germans could have actually captured Verdun and given the public a tangible triumph perhaps they would have left Falkenhayn in charge for the duration. As it was his strategy only appeared to produce horrendous casualties without winning any major victories.
That was part of the problem. They couldn't, but it wasn't necessary for the plan to work. The public might have wanted it, but like at Cold Harbor the public wasn't privy to the strategy behind the operation, nor was much of the army, for security reasons. But ultimately the plan was sabotaged by faulty intelligence that suggested the French were actually being ground to pieces, though they really weren't. Had Falkenhayn known the truth he would have abandoned the operation and focused on something else, saving his job and probably Germany.