Grant was an excellent strategist as well. Did he make mistakes? Sure, and so did Lee. Grant knew how to use the advantages the union had in men and material and motivate his troops just as Lee knew how to make the best of what he had to work with.
What you put down as Serman’s “fame” is mythology as well, put forth by the defeated as an excuse for why they lost. It is pretty arrogant and ignorant to believe that the opposing force is not going to march into your territory and remove the means to continue to support your troops. Using that logic would say that allied forces should have stopped at the German border during WWII. You destroy the opposing forces ability to provide for their troops.
Starving little children and murdering old men. Celebrate Sherman all you care to.
Both were excellent tacticians but I would give Grant the edge because he really never made the same mistake twice. Lee's mistakes at Gettysburg mirrored his loss at Malvern Hill and the North's loss at Fredricksburg. Attacking an army which was dug in on higher ground generally proved suicidal in the Civil War. With regard to strategy Grant was flat out superior. I don't really find much strategy at all on Lee's part at all other than to invade the North twice and both campaigns were failures and accomplished nothing but to weaken the South. The Gettyburg campaign never should have been undertaken and Longstreets plan to devote more resources to the Western campaign instead was the better play.
Southern complaints about Sherman are disingenuous. Honesty would compel them to complain of the refusal of Hood and Wheeler to defend Atlanta and Georgia.