Question

What was the most significant benefit to the Union of the siege at Vicksburg?

The Confederacy was completely bankrupt by the siege.
The Union victory essentially divided the South in half.
Confederate troops withdrew from states to the west of Mississippi.
Lincoln was able to enforce the Emancipation Proclamation in parts of Mississippi.

Answer 1

The Union victory essentially divided the South in half.

Vicksburg was the Confederacy's last stronghold on the Mississippi River.  The Union victory and capture of Vicksburg cut off the Confederacy states of Texas, Louisiana and Arkansas (west of the Mississippi) from the remainder of the Confederate states east of the river.

Answer 2

divided the south in half