I think had the AoP not been as "ponderous" and tied to its logistical trains, etc., Grant many have had more success in the execution of his early plans.
For the most part Grant operated in the West with smaller armies, with less artillery and much less cavalry, and usually with reliable, consistent river supply lines. (Cavalry and artillery require a much greater rate of supplies per soldier because of the horses.)
For example, the swift movements of the Vicksburg Campaign involved almost no cavalry operating with the AOTT and total forces half that of the AOTP in 1864 (Grant's army was significantly reinforced during the siege.)
AOTP, including IX Corps, was over 100,000 men with a large cavalry corps and substantial artillery train, in territory picked clean of provisions, with no railroad and limited help from rivers for supply.
Sherman worked for Grant. Sherman was doing what he did because of Grant's orders. So was every other army commander in the Union army.
By that logic, Lincoln took Savannah.
Grant appointed Sherman and approved Sherman's strategy. The strategy was Sherman's, and the details of logistics, tactics, and execution where Sherman's and his staff & subordinates.