Interesting observation that may not coincide with what actually played out. In Virginia, Grant clearly instructed Meade to go after the ANV, and not Richmond. Consequently, the AotP's flanking maneuvers were intended to get around Lee's flank in an effort to destroy that army. Yet in Georgia, Sherman's flanking movements around the AoT were a sort of a game of cat and mouse with the end goal of leading the AotT to Atlanta. The biggest proof of this is twofold. 1) The fall of Atlanta (and not the destruction of the AoT which of course was not accomplished by Sherman) was a major blow to the south and was perhaps a key factor in enabling Lincoln to be re-elected. 2) Sherman basically ignored the AoT after besting it in a series of battles around Atlanta; while Hood took the intact AoT in a retrograde movement to derange the W&A RR line and attempt an offensive into Tennessee and beyond, Sherman went in the opposite direction on his March through Georgia.
Clearly, the war in Georgia indicates that sometimes the seizure of an important enemy city was a critical goal for the Union.