Well, with what little I have read about him and the US Civil War, my € 0.02.

Robert E. Lee was a superb commander and IMHO on par with Grant. He had the luck though to have some superb subordinates (like Jackson, Longstreet), and some incompetent, or at least flawed opponents.

McClellan should have destroyed his army at Antietam, should have beaten him to Richmond, Burnside should have never attacked him at Fredericksburg (though Burnside had him beaten strategically initially, but was hampered by bureacrats as far as I know) , and Hooker simply lost his nerve when something unexpected happened.
When Meade arrived the Army of the Potomac finally had a commander that knew how to use his numerical superiority and superiority in equipment. Meade had shown good military skills, as his units were among the more succesfull at South Mountain, Fredericksburg and Chancellorsville, as well.

Also, as the war progressed, Lee was facing odds that were too big. It is IMHO quite amazing that he held out as long as he did.

I do not know for sure, but IIRC he actually caught Grabt at Wilderness. Only the terrain prevented him from reaaly exploiting it.

IMHO Grant was the lucky guy during the war. Yes he got Donelson and Henry, a superb achievement. Yet he almsot got his army killed at Shiloh (what saved him, IMHO was Johnson getting shot and some of Johnson's subordinates messing up his battleplan). IIRC this almost happened again at Wilderness. When Grant took over the Army of the Potomac, he inherited an army that had already gottten rid of many of the incapable officers earlier in the war. He inherited an army in fairly high spirits, under a commander who had beaten Lee decisively. He also fought an opponent that was, in virtually all respects, inferior by quite a large margin to his own army. And yet he had a lot of trouble defeating the Army of Northern Virginia.

My guess as to why Lee ordered Picket's charge is that he knew it was the last chance for the Confederacy to gain a decisive victory against the Army of the Potomac. That, he actually might have thought, or realised, that by that time a new breed of commanders had taken over the Army of the potomac, and the other Union armies.... and that the advantage in size and equipment the Union armies had was going to tell a lot more.
Also, J.E.B Stuart was supposed to swing around the AoP.

Grants biggest contribution is laying down the foundation for US military doctrin. Keep presure, and use advantages in size and equipment. And try to make these advantages as large as possible.

Meade's main contribution was, IMHO, not losing the battle of Gettysburg, and not squandering the victory. In a way similar to what Montgomery had to do and did at El Alamein.

Note: This is just my opinion, based on quite limited reading, seeing documentaries and following discussions on the internet. And to that my own logic applied. I am quite sure that there are quite a few on this board with a much greater knowledge. I do intend to learn a lot more on the US Civil War though.