Lee was probably the better general.  But Grant was plenty good enough to get the job done. 

Grant is usually downgraded because of the summer campaign of 1864. Buy Grant was not the direct commander of the Army of the Potomac, Meade was. The same Meade who had allowed Lee - with a third of his army casualties - to escape after Gettysburg. the same Meade who forgot to fully man Little Round Top at Gettysburg, the Union Army only being saved by the bravery of Joshua Chamberlain and his Maine troops. The same Meade that was so afraid of what Lee might do, that he proceeded too cautiously, allowing Lee twice to have enough time to reinforce troops about break at the Wilderness and Spotsylvania. Grant himself complained about his subordinates inordinate fear of what Lee might do:

"Oh, I am heartily tired of hearing about what Lee is going to do. Some of you always seem to think he is suddenly going to turn a double somersault, and land in our rear and on both of our flanks at the same time. Go back to your command, and try to think what are we going to do ourselves, instead of what Lee is going to do."--An uncharacteristic burst of temper from Grant when being reminded repeatedly of the powers of Robert E. Lee.
http://faculty.css.edu/mkelsey/usgrant/bygrant.html

We often forget that Grant twice - three times if you count Appomattox - captured entire Confederate armies. At Fort Donelson and at Vicksburgh. Besides defeating the Confederate Army of Tennessee and opening the way into the heartland of the Confederacy.

Lee was made so seem great by a succession of timid and incompetent Union commanders. McClellan right at the gates of Richmond - and retreating after one set back. McClellan having Lee's operational orders in hand at Antietam, knowing Lees forces were split, and instead of defeating his army in detail, fought the battle in such a way as to allow them to recombine. Burnside going across and open field and attacking up a hill, against troops in a fortified position at Fredericksburg. Hooker panicking at Chancellorsville  against a force half his size.

Grant. He simply used the brutal realities of warfare...I have more men, more material and the South doesn't.

Lee was good but largely because of Thomas "Stonewall" Jackson if you notice, there was a big change in the South's victories after his death. It is doubtful Stonewall would have allowed the invasion of the North (Gettysburg) which was the Confederates downfall.


Billy

But Gettysburg was the second time the South invaded the North, and McClelland caught Lee at Antietam, because he had Lee's operational orders in hand (and even then blew it). I think without the luck chance of having the order fall into his hand, Lee would have simply continued into Pennsylvania. And Stonewall would have favored the Gettysburg campaign if for no other reason than it allowed Southern Armies to live off the North for a change. The question is would Stonewall have talked Lee out of attacking at Gettysburg, or into breaking off the attacks after their first lack of success?

Do you think Lee would have survived at Antietam, if Lee's orders had fallen into the hands of Grant, Sherman, Thomas, Schofield or Sheridan. The South won one major battle in the West, Chickamauga. The lost or at best tied, every other one. Grant missed his Western subordinates when he went East, as much as Lee missed Jackson.

We can play "what if" to death, but if Jackson had been at Gettysburg Culp's Hill would most likely have been captured the first night...so long to the fish hook.

Lee was a Napoleonic general. The problem was that the weaponry no longer allowed for Napoleonic tactics. In Napoleons day, muskets took so long to reload, and were so inaccurate; an infantry charge could break the enemy's line. By the civil war, rifled muskets and cannons made that impossible. You were taken under fire at too long a range to ever get the momentum necessary. When Lee ordered Ewell to attack Culp's hill Ewell had already lost a quarter of his troops driving the Federals from north and west of Gettysburg. And he had driven them into a better position. High ground, with cannon parked wheel to wheel and reinforcements steadily coming up. In addition, I believe at that time Rock Creek was dammed, in order to use the water for some industrial purpose, which meant there was a deep pond to his left which prevented flanking the federal position. In any case, Lee had won battles due to federal incompetence or his federal opposite number panicking. Meade wasn't brilliant, but he was cautious. He knew he was in perfect defensive position (even if he forgot to man Little Round Top, neither side had noticed it yet). And of course, without Stuarts calvalry, Lee was effectively blind in enemy territory. I must note that Ewell only had half the troops Jackson would have brought to the fight, as Lee had divided Jackson old Corp into two corps, under Ewell and AP Hill.

Lee had far better Commanders at his disposal. Grant was handed a stacked deck and made the most of it. In today's battlefield, Grant would be hands down a better General.

The unions best generals, were usually in the West. It's interesting, in describing Grant; Sherman said he had: "two o'clock in the morning courage. You could wake him up at two in the morning, and tell him his flank was being turned, and he would be just as calm and unperturbed, as if it were a just another minor setback". How many of Lee's victories depended on his opponent panicking and doing something stupid. Like Hooker at Chancellorsville or McClelland during The Seven Days.

In mention of Picket's Charge, it was rumored that Lee had a mild stroke at the time, so he definitely wasn't at the top of his game.

On a completely different tangent, in a game of Victoria 2 as the USA the Confederacy placed Lee in the west and completely abandoned Virginia!  Lee wouldn't be happy about that...  In fact he wasn't, because in late 1861(the war lasted from Oct. 1860- May 1862) Lee turned his 33k army east towards Virginia where I had the majority of my Army  !   The last stand of the Confederacy took place in Alabama by the way...  Sorry about going off-topic but that was the most epic game I ever played.

If the Confederacy was going to abandon Virginia, why was he fighting on the side of the Confederacy. Only once did he allow, a major portion of his army - Longstreet's Corps - to go west and help the confederacies beleaguered troops. That resulted in the Confederate victory at Chickamauga, and the siege - and near destruction - of Rosacran's army in Chattanooga.  Besides abandoning Virginia would have opened the way int North Carolina, who hadn't really wanted to secede, and East Tennessee which was pro unionist, as was much of the Appalachian region. And of course without Lee, Whats to prevent the Union from simply marching down the eastern seaboard?