Big Theology, in my view, treats Big History as sacred scripture, and then debates how we should live our lives based on this scripture.
Big History contains the sacred scriptures of all the world’s religions, as well as the histories and practices they initiated after their creation.
“Small Theology” assumes the truth (or at least value) of particular scriptures and histories, and then debates the ramifications of those assumptions. Partisanship plays a big role here: as a Christian, I need to be able to argue why I think “Christianity” trumps Buddhism or Daoism or Islam or other competing religions as a better way to live one’s life. And if I can do this in a “friendly” way, and am willing to learn from the advocates of other perspectives, I can only gain.
“Big Theology” takes a step back and treats all sacred scriptures as parts of the mega-narrative of Big History. “Big Theology” takes the facts about all of these scriptures (when were the written? by whom? why? what has been their subsequent effect on the Big History narrative?) and ascribes them a relative value, or looks for convergences that be assimilated into a “bigger” theology.