As an aside, Lee absolutely supported slavery; a certain performed distaste for the institution was quite a la mode for Virginia planters, but it certainly didn't stop them from making money off the institution or fighting to defend it.

As to who was the better general, it's a complicated question. It's not like when you're testing the acidity of a substance, where you can just put a chemical strip in it and see what color it turns; we can analyze their tactical and operational performance, but there's no way to conduct controlled experiments or quantify results. As historians, we're limited to what happened, and we never got an even matchup between Grant and Lee.

That said, I think the Overland campaign was an extremely strong tactical showing from Lee, and that Grant made some highly questionable decisions during it.

For one, I am not convinced of the superiority of an overland approach compared to the Peninsular campaign. The Union had almost total control over the rivers and ocean, so it's basically an invulnerable supply line, and it heads straight into Richmond. Lee's army is dead in the water if Richmond falls; the next place the army could be supplied would be along the Roanoke river in North Carolina. Barreling straight for Lee's army shows rather simplistic thinking on Lincoln's part, and Grant should have argued more strongly for his planned raid/amphibious turning movement through North Carolina.

I think Grant did not manage his subordinate commanders as well as he could. Things quickly soured between him and Meade, especially since Grant undermined Meade's authority over Sheridan. Meade wanted to keep the cavalry with the army to screen his movements and Lee's while Sheridan wanted to go off on raids into the enemy rear area. To me, the experience of the Civil War shows the value of having the cavalry operate with the army; Lee had it with him and won Chancellorsville, and when he let Stuart ride off on his own, he lost Gettysburg. Hooker at Chancellorsville had his cavalry off on a raid, and lost, and Meade had it with him for Gettysburg, and won. Undermining a key subordinate's authority for operationally unsound reasons is a black mark next to a commander's name in my book.

Furthermore, when the campaign actually commenced, Grant took too long crossing The Wilderness, against the advice of the men planning the army's movements in detail. This allowed Lee to nullify the Union's artillery advantage with a close in knife fight. Lee set his corps commanders up for victory, but A.P. Hill fumbled his defense astride the Orange Plank Road, and Longstreet was badly wounded when the battle was at its height. He had 'rolled [Hancock's corps] up like a wet blanket', and was poised turn the U.S. flank and drive into their rear along the Brock Road, but the attack lost momentum with his wounding, and the battle ended as a tactical stalemate.

What strikes me most about the campaign as a whole was how many good commanders Lee lost. Jackson was killed last year, and Longstreet was wounded only a couple miles from the same spot. Jeb Stuart was killed, A.P. Hill had a habit of falling ill at inopportune moments like thee Battle of the North Anna, (prostatitis, result of a 'youthful indiscretion' at West Point), where Ewell suffered a mental breakdown at the same time Lee fell ill. The North Anna is a river with a notable bend in it; when Grant's army crossed, the bend divided it into three elements, which a bold commander could attack and defeat individually. He repeated from his cot that they needed to 'strike a blow', but there was no one to strike it. Not only was Lee commanding an army in desperate straights, but he also had to manage his corps commanders quite closely, and with Stuart's death, he had to command the cavalry in some detail as well. It's said that during the Overland Campaign, Lee never got more than two consecutive hours of sleep; under that kind of strain, and without your best lieutenants, it's hard to get the most out of an army.

Coming from the West, Grant seemed to fundamentally misunderstand the tactics that evolved in the east. In his experience, resorting to defensive works was a sign of an army's weakness or timidity; an entrenched army to him was already half beaten. Commanders in the east, however, used field fortifications as simple economy of force measures; this led to costly miscalculations like the assault at Cold Harbor, where the U.S. suffered thousands of casualties to no end. To me, this flaw was of grave importance; 1864 was an election year, and immense bloodshed without decisive results could seriously endanger Lincoln's prospects of reelection, and thus the whole war effort. In the end, this approach did not prove fatal to the political side of the war, but it can't be ignored when assessing the two.

This is not to say it was pure chance that decided the campaign; Lee made errors of judgement, and Grant had a great grasp of maneuver principles, which he had earlier demonstrated in the campaigns in the west. The Overland campaign tends to get portrayed as direct and purely attritional, but Grant consistently tried to outflank Lee. He did not get a crushing flank attack on the tactical level, but these turning movements were able to lever Lee out of strong defensive positions. Lee made a serious error when he misread the signs at the Battle of Spotsylvania; his army was deployed in a long salient called 'the Mule Shoe', and after driving back the U.S. attack on May 10, believed they were planning on withdrawing. He ordered Johnson's division to prepare to march for a possible counteroffensive, packing up their artillery; Lee did not know that rather than a withdraw, Grant was planning an all out attack on Johnson's division and Ewell's corps in the Mule Shoe. As a result, on May 12, Hancock's attack broke into Confederate defensive works, though desperate counterattacks prevented them from breaking through. A hefty share of total Confederate casualties from the battle were prisoners captured during Hancock's assault on May 12.

Furthermore, Grant did an excellent job setting up his crossing of the James river, which allowed him to threaten Richmond and Petersburg. He used the Army of the Shenandoah to threaten Lee's supply line and divide his army, and used Sheridan's cavalry to draw off Lee's. He then stealthily withdrew from his positions outside Cold Harbor, and had a really well engineered bridge constructed over the James. Beauregard's strong defensive performance in Petersburg prevented it from being captured in the first assault, but the U.S. settled into a siege, and maintained it despite all attempts by Lee to break the stalemate.

In the final analysis, Grant pursued an ultimately successful strategy, using maneuver, deception, and the operational art to contain Lee's army in Richmond and Petersburg, which led to its eventual collapse. This strategy ultimately depended on having superior numbers; he needed to have enough men to block a counteroffensive towards Richmond as well as enough for a credible turning movement. He needed to have substantial field armies in the Shenandoah, the Peninsula, and northern Virginia to successfully divide Lee's army. It's important to keep in mind, though, that generals employ strategies based on what they have; there's no reason to strategize like you have a smaller army when you don't.

Fate also played a role; the loss of so many experienced senior officers in the Army of Northern Virginia seriously hindered its performance. Ultimately, Lee proved unequal to the task, while Grant accomplished his. Lee's was the greater task, and he had less with which to accomplish his, while Grant's was more modest, and he had greater means at his disposal. In terms of who was the better general, that's an ultimately unknowable question.