While Grant and Lee were engaging in non-stop combat in Virginia, a different type of campaign by different types of generals was getting underway. Sherman, leading an army group consisting of the 98,000 men of the Army of the Tennessee, the Army of the Cumberland and the tiny Army of the Ohio, confronted the 60,000 Confederates of the Army of Tennessee under General Joseph Johnston. Both Sherman and Johnston were more strategists than tacticians, military chess players rather than great captains of the battlefield. Johnston especially had good reason to fear the result of a battle going against him. His army, and his army alone, stood between the vital interior of the Confederacy, thus almost entirely untouched by the War, and Union conquest. Sherman understood that there were many excellent defensive positions between him and Atlanta, and if he was going to get there he had to depend more on maneuver than direct attacks.
The first battle of the campaign, Resaca, reflected in miniature the course of the Atlanta Campaign so long as Johnston was in command of the Army of Tennessee. Skirmishing occurred on May 13 in front of the hills around Resaca where Johnston had a well-fortified position. Fighting on May 14 produced stalemate. On May 15 the fighting resumed with no advantage, until a Union turning movement on the Confederate left threatened Johnston’s railroad supply line. Johnston retreated in good order. This sequence would be repeated time and again as Sherman moved methodically toward Atlanta and Johnston kept a sharp eye out for an opportunity to defeat a portion of Sherman’s army as Sherman maneuvered. Casualties were approximately 4500 for the Union and 3800 for the Confederates, high enough for the killed and wounded men, but barely of note in the scale of loss being set in the Eastern fighting.
The Atlanta campaign is a fascinating one for the reasons you outline. Both were mediocre tacticians, but superb at the operational level.