Describe the strategic objectives of the Confederate armies at the Battle of Gettysburg and the Union armies at the Battle of Vicksburg. Which battle was more important outcome for the Union in winning the war and why.
With the onset of the Civil War, the South's objective was to defend the South. Eventually, the war had progressed far longer than either the North or the South had anticipated. The South needed to place more political pressure on the North with a victory on northern soil. General Robert E. Lee's goal was for the South to succeed in a major campaign in the North, and then the North would have to consider a settlement. In addition, a southern victory would potentially sway support to the south from England.
At the same time, a major victory in the South would further reduce the likelihood of the South being able to continue with the war. The North already had the advantage of greater numbers and greater access to weapons and materials. A devastating loss for the South would force an eventual surrender.
While both losses were crucial blows to the South's likelihood of winning the war, the loss at Gettysburg was most devastating. The South was lacking in resources and men, and the march back to the South would be long, difficult, and lacking in pride. Such a loss would no longer sway help from England to the South's side. In addition, the South would have to carry on with limited resources, which only hinted at an eventual surrender.
At the Battle of Gettysburg, the South had invaded Pennsylvania. The South was not really trying to invade and occupy the North. Instead, its strategic goal was to push the North to negotiate. If the South could successfully invade the North, the North would have to pull troops from the South to repel the invasion. This would make it much harder for the North to win the war militarily and it might be persuaded to negotiate an end to the war.
The Battle of Vicksburg had to do with control of the Mississippi River. Vicksburg was the key to control of much of the Mississippi. The Confederacy needed to hold Vicksburg so that it could continue to use the river as a supply line. It needed to be able to move supplies from the western part of the Confederacy to the East. If Vicksburg was lost, the South would be cut in half and the eastern half would lose access to the supplies of the west.
There is no clear answer as to which of the battles was more important. My own feeling is that Gettysburg was more important. I would argue that a successful invasion of the North would have caused the North to pull its troops out of the South. This might have given the South the opportunity to retake places like Vicksburg. This makes the loss in Pennsylvania more important than the one at Vicksburg.