It has been said (I think correctly) that Lee was the last of the great old-fashioned Generals, and Grant was the first of the great modern ones. They were fighting two different wars - Lee, the chivalrous, tactical duel of soldiers; Grant, the modern "total war."
They both had their early wartime experience under Winfield Scott in the Mexican War. NOBODY can dispute that Lee was clearly Scott's favorite, Grant and every other commander in the country knew it. Lee's record at West Point is a legend to this day and Lee's strategies have been studied for 140 years (I am fairly certain that Rommel was a student of Lee's tactics). Grant fought the modern all out war because he could, Lee never had the opportunity.