Grant was a mediocre soldier, and largely a failure as a citizen. He came into his own as a general when Lincoln recognized that sometimes sheer tenacity wins wars. In contrast to the “feint-and-withdraw” complacency of Maclellan, Grant was a steady, driving force that pounded onward even against repeated resistance. He knew he could defeat the Confederates just by wearing them down.
Lee was the tactician — and a brilliant one. Grant was the strategist, more determined than brilliant.
Mediocre? Won the American Civil War and won two terms as president is mediocre? Phew.
Mostly, he just had more audacity than the Generals he was facing. The battles he was in were some hair raising affairs - if McClellan had a pair he would have beaten Lee in the Seven Days and the war would have been over in 1862.
Chancellorsville was a brilliant victory, but not every battle Lee fought was like that.
Sure, Lee was a competent commander -- and more -- but his reputation is a result of the incompetency of the generals he faced.
It didn't take genius to win the Battle of Fredericksburg. And if McClellan or Meade had followed up on Antietam or Gettysburg they could have dealt Lee mighty blow.
To turn back McClellan in the Seven Days' Battles near Richmond, Lee took bigger casualties than McClellan.
So whoever was going to beat Lee would have had to lose even more men.
There wasn't some way of winning a victory through pure ruse, finesse, and maneuver without actual battles and major losses.
Grant was fighting in a way that could win the war, something that Lee wasn't doing -- and maybe couldn't do, given the resources available.