Personally, I'm not sure about Sovngarde as the Underworld. It makes sense if you take the Underworld to mean "afterlife," but symbolically and mythically its http://en.wikipedia.org/wiki/Underworld. If we take http://en.wikipedia.org/wiki/Death_in_Norse_paganism#Afterlife Sovengarde is Valhalla, and the "underworld" would logically be more akin to Helheim. Though I personally associate the word with the Greco-Roman Hades instead.
Anyway, standard disclaimer: I'm just guessing.
The only sources that even mention the Underworld are
Five Songs of King Wulfharth and
Varieties of Faith in the Empire and both only reference the Underworld in relation to Shor. It was my guess that Shor is trapped in the Underworld, which he remade to become his personal realm of Sovngarde. Indeed
Varieties of Faith defines Shor as the God of the Underworld, implying that he has control of the place. In this fashion he remade the the realm using CHIM or lent-bone creation to change it from Hel or Nifhel to Valhalla or some form of Asgard. If we had to make a direct comparison, I'd say that Sovngarde is Asgard with Shor's Hall being Valhalla and the Dreamsleeve being Yggdrasil.