I wish there were more specifics about substance of the debate. For the most part, it seems Chesterton won because he came off as “nicer” than Darrow. That almost sounds like today’s debates, in which style often defeats substance. The only real clue about what happened was that Darrow was apparently debating a straw-man instead of Chesterton; and Chesterton apparently didn’t let him get away with it.
No doubt there was a large component of "the nice guy won." I think we all naturally favor the man that remains calm, witty, and humorous. And yes, Darrow did attack the "straw man" of a strictly literal approach to the Bible. That was his hammer against William Jennings Bryan at the Scopes trial and likely he assumed, since Chesterton was Orthodox Christian, that Chesterton would take the same approach.
That is why Darrow was completely thrown when, after making his case that a strictly literal interpretation of the Bible was silly, Chesterton agreed and then proceeded to defend Orthodox doctrine sans the literalist approach.
Darrow also came to defend science but found that his opponent was far more knowledgeable about science than he was.......
Mrs. Frances Taylor Patterson also heard the Chesterton-Darrow debate, but went to the meeting with some misgivings because she was a trifle afraid that Chesterton’s “gifts might seem somewhat literary in comparison with the trained scientific mind and rapier tongue of the famous trial lawyer. Instead, the trained scientific mind, the clear thinking, the lightning quickness in getting a point and hurling back an answer, turned out to belong to Chesterton. I have never heard Mr. Darrow alone, but taken relatively, when that relativity is to Chesterton, he appears positively muddle-headed.”