Wonderful question! Tacticaly Grant because he changed the way the War Between the States was fought, but strategicaly Sherman because he changed the way future wars were fought. The nod goes to Sherman.
Ulysses Sherman Grant died in 1932.
Ulysses Sherman Grant was born in 1867.
Sherman
General Sherman wrote about his reasons of concern for his friend US Grant at the Siege of Vicksburg. Sherman believed that Grant was working and hampered by Northern public opinion. So much so that Sherman feared Grant would abandon the effort to capture Vicksburg.
Because Sherman had proved himself a competent General who had given good service to Grant. They were also good friends. In his memoirs, Sherman said "He stood by me when I was mad. And I stood by him when he was drunk."
Sherman carried credibility with Grant, tested under fire, and was a trusted friend.
To change the course of the war. Grant and Sherman both believed that it was the strength of the people's will that was keeping the war going.
Grant and Sherman
William Sherman
Grant to Sherman: "Make Georgia howl!"
Principally U.S. Grant. Sherman owed his promotion largely to his personal friendship with Grant. Later he reflected "I looked after him when he was drunk, and he looked after me when I was mad."
In may of 1864 general grant ordered general sherman to march his army out of chattanooga into Georgia.