Lee's reputation for daring comes primarily from necessity: He generally had fewer men and fewer resources, so he had no choice but to take long chances. This led to his having to be bold, but by watching Lee's performance at Gettysburg, as well as Sharpsburg, I don't see him as a particularly innovative commander. Able, yes. Driven, yes. Dedicated, definitely. Intelligent, beyond doubt. But essentially, Lee was tactically conservative, and strategically didn't grasp how crucial the western theater was in terms of the Civil War as a whole.
THAT MUCH SAID....I do admire General Lee immensely, and were I a soldier of that time, I would not hesitate to follow Lee into battle.
Grant, however, was cut from an entirely different mold from Lee. Grant wasn't the "Marble Model" that Lee was. He had been a middling student, but was a personally brave officer. The small and gossipy nature of the Army of the 1850s had more to do with Grant's reputation as a drunkard than his actual behavior does (my theory is that the wife of some other officer in Grant's regiment wanted the prestige of being married to an officer of higher rank, and so started the rumors of Captain Grant being an alcoholic in the aim of getting Grant busted. I've seen officer's wives in the modern military try similar stunts today, so that's where my theory comes from). Grant understood tactics from the level of a company grade officer, whereas Lee understood them from the level of a field grade officer. This contributed to their styles of command as generals.
Grant knew that to win a battle you took territory, but to win a war you had to destroy your enemy's means to prosecute that war. This is elementary to us today, but was radical thinking in the 1860s. Officers were schooled in the thought of Henri Jomini, a Swiss theoretician who taught that wars were won by taking objectives, not by killing more of the enemy's soldiers than he killed of yours.
Grant practiced maneuver warfare wherever possible....his Virginia Campaign of 1864 was one series of left flanking assaults against Lee. This is similar to how he handled Vicksburg. Grant tried to isolate Vicksburg by maneuver, but was unable to accomplish that, and thus settled into a siege. Grant understood the value of siege warfare, but it was always his final option, not the first. Compare that to McClellan, who believed in the siege as being the highest form of warfare because it focused on a geographic objective, not open field battle.
The breakout from Petersburg in 1865 was a further example of maneuver warfare. Grant always tried to hit Lee on the flanks, or to encircle him. Yes, Grant lost more men than Lee, but this is because of two reasons: Grant had a bigger army, and Lee had to husband his men carefully DUE TO HAVING FEWER BACK HOME TO DRAW ON. When Lee was in a situation where he was not outnumbered, he spent men to the same extent as other commanders during the Civil War.
My whole point is that Lee and Grant are BOTH officers and commanders to be proud of. Lee represents the best of the Old Army...the tradition, the valor, the legend. Grant represents the New Army...mobile, aggressive, dogged and determined. Think what an army the US would have had with those men on the same side....and to an extent, that's what we have now...the Rebs and the Yanks all in US camo. Hell of a good Army. Best on Earth.
(Great great grandson of a sergeant in the 9th Texas Volunteers, 1861-1865, CSA)
Grant was a proto-Eisenhower, a general who loved broad pressure and attrition. That's hardly brilliance. Sherman, on the other hand, was a proto-Patton.