Right: Briseis led to Agamemnon's tent by two heralds
Left: Elders conversing

Here are the two sides of the vase side by side. Do you detect any differences in the way Briseis is depicted on the different sides of the vase?
Here's how the sequence of figures runs starting from side a (left above): Briseis and two heralds; Patroclus, Achilles, Phoenix; three elders; Briseis and two heralds. Thus, Briseis led from Achilles' tent and Briseis led to Agamamnon's tent face each other on either side of the handle.
Below are details of Briseis and the heralds on the two sides of the vase in the way that they would face each other.

to Agamemnon's tent

 

from Achilles' tent