His was right. The battles in the West were more consequential as it deprived the confederacy more material support from it’s own resources as well as the transportation needed to get it to where it was needed. Lincoln’s Anaconda strategy slowly strangled the Confederacy.
Blockading the important pots of New Orleans, Mobile, and Charleston and capturing the waterways of the Mississippi, Tennessee and Cumberland rivers denied cheaper transportation of men and material for the South and flipped this advantage to the Union. Same with the railways, such as they were, in Nashville, Chattanooga, Atlanta and Corinth hurt mobility of southern troops and supplies.
The war in the east was a continuous string of battles that exchanged comparatively little terrain or tactical advantage until the last year of the war when Lees army was starving for men and material denied him by Union victories in the rest of the south.
Vicksburg was also important as it brought Gen. Grant back east.