Grant never beat Lee on a battlefield on equal terms. Grant overwhelmed Lee with superior manpower and firepower.
In my house, my father is a Grant man and I am a Stonewall Jackson person...so I have heard alot about Grant. There was military genius in Grant. It was different from Lee, but it was there.
Lee would not allow anyone to say anything negative about Grant after Appomattox.
But beat him Grant did. He fought Lee toe-to-toe, kept him on the defensive, robbed him of the initiative, and finally bottled him up in Petersburg.
As for Lee, he lost pretty convincingly up at Gettysburg, to an army of roughly equal size, and to a general that few would consider his equal. In fact, Lee lost to inferior generals to end both his campaigns in the North.