General Grant was not an alcoholic. He drank missing his wife. He never drank while in battle. That's one of many slanders of the Lost Cause that victimizes the South as well as proposes the South to be superior in many aspects.
Grant was by far the better general. While Lee fought a mostly defensive Virginia campaign, Grant was out completing the North's military objectives in aggressive, modern strategies. His rally and subsequent victory at Shiloh, despite his mistakes. His Vicksburg Campaign that is still studied to this day. Grant's ability to fight the war that Lee could not win when Grant finally took over the army of the Potomac and hounded Lee, when previous generals would turn, until he had nothing but a ragged army.