I have a theory.
We know(from the jaghut, MoI iirc) that Hoods realm is not the only realm of death, only the most recently. Any older culture, will have its own. Jaghut don't go to Hoods realm for example.
Hood does not take the andii. Their god, is mother dark. She is the one who their souls seek.
Except she is ever turned away.
A quote, to illustrate my point.
Toll the hounds, on bantam press, page 694, harback, said:
And now your soul waits, as it must. For this is the fate of the Tiste Andii. Our fate. We will wait.
Until the wait is over.
Nothing awaits their souls. Mother dark does not take them. Her great betrayal. This, I believe, is what the andii lost.
They do not face oblivion, as the T'lan Imass. I imagine they simply wander. Searching for Mother Dark. Who is ever turned away.
Not only that, but the Tiste Andii have many years longer, and the T'lan Ritual seems to stop the Imass feeling much emotion. That is their sacrifice.