This event wasn't a debate so much as one lecture followed by another one.
Berlinkski takes at least twenty minutes to get around to something like an argument, but he speaks well and tells a good story about magical thinking and scientific progress. He isn't arguing for theism, he is arguing for the legitimacy of the inference to design, both in biology and cosmology. His argument is essentially this: If we cannot yet explain something scientifically, such as the initial conditions of the universe, or the very first living things, or the world of mathematical abstractions, then it may be rational to infer that there is indeed mind behind the universe. To paraphrase Stephen Colbert paraphrasing Bill O'Reilly, "God exists, because I don't know how stuff works."
Underdown points out the difficult of putting God into gaps, namely, that the gaps keep closing and new ones keep opening up. If God lives in episemtic gaps, he surely skips about quite a bit. He also tries to put science (as a field) into historical perspective, and replies to a few more of Berlinksi's points