The actual record shows that "brilliant" Lee lost more men in battle than "butcher" Grant, especially when Lee was on offense.
Yes, the nature of 19th century warfare dictated entrenched defense had a huge advantage over mobile units on offense, and Lee took advantage of that by war's end.
But in the beginning, when Lee was on offense at, say, Antietam or Gettysburg, his losses in losing those battles were greater than Grant's in winning his.
During the war, Lee had three commands -- first in West Virginia, then North Carolina and finally Virginia.
In all three Lee failed.
Grant also had three commands -- first at Forts Henry & Donelson, then Vicksburg and finally Virginia.
In all three Grant won "unconditional surrender" from his opponents.
Grant's performance made him hugely popular with Union voters who elected him President, twice, at their first opportunity.
So "Grant the butcher" is propaganda which people of his time knew to be untrue and people today can soon learn with a little effort.
And no, Lee's losses at Gettysburg and Antietam did not amount to the nearly 70 thousand that Grant pissed away in the Overland Campaign.