Some of Green's comments are confirmed in a letter from Balfour Stewart to David Forbes on July 4, 1860. He wrote The Bishop said he had been informed that Prof. Huxley had said that he didn't care whether his grandfather was an ape ….
Here is part of a letter that Huxley wrote to Henry Dyster on September 9, 1860.
Samuel thought it was a fine opportunity for chaffing a savan [sic] — However he performed the operation vulgarly and I determined to punish him — partly on that account and partly because he talked pretentious nonsense. So when I got up I spoke pretty much to the effect — that I had listened with great attention to the Lord Bishop's speech but had been unable to discover either a new fact or a new argument in it — except indeed the question raised as to my personal predilections in the matter of ancestry — That it would not have occurred to me to bring forward such a topic as that for discussion myself, but that I was quite ready to met the Right Revd. prelate even on that ground — If then, said I, the question is put to me would I rather have a miserable ape for a grandfather or a man highly endowed by nature and possessed of great means of influence and yet who employs those faculties and that influence for the mere purpose of introducing ridicule into a grave scientific discussion — I unhesitatingly affirm my preference for the ape. Whereupon there was inextinguishable laughter among the people — and they listened to the rest of my argument with the greatest attention. … I believe I was the most popular man in Oxford for full four and twenty hours afterwards.
Huxley's wording “If then, said I, the question is put to me” seems to imply that the question wasn't put to him. Clearly, Huxley thought he had put the Bishop in his place.
Wilberforce also thought that he was the winner in this confrontation. Here is what he said in a letter to Sir Charles Anderson on July 3, 1860
On Saturday Professor Henslow … called on me by name to address the Section on Darwin's theory. So I could not escape and had quite a long fight with Huxley. I think I thoroughly beat him.
Little is known about how the audience as a whole viewed the event. However, it is doubtful that it represented an overwhelming victory for Darwinism as is sometimes portrayed. First of all, the audience contained a large number of clergy who were opposed to Darwinism. In addition, it is known that one of the early converts to Darwinism, Henry Baker Tristam, de-converted as a result of the discussions following Draper's talk. Alfred Newton, who was responsible for converting Tristam to Darwinism, said that Tristam “waxed exceedingly wroth as the discussion went on and declared himself more and more anti-Darwinian.”
The traditional account implies that Wilberforce based his arguments largely on scripture. That is not likely. Five weeks earlier Wilberforce had written a review of Darwin's Origin of species, which was published in the July issue of The Quarterly Review . In this review he states the following
Our readers will not have failed to notice that we have objected to the views with which we are dealing solely on scientific grounds. We have done so from our fixed conviction that it is thus that the truth or falsehood of such arguments should be tried. We have no sympathy with those who object to any facts or alleged facts in nature, or to any inference logically deduced from them , because they believe them to contradict what it appears to them is taught by Revelation. We think that all such objections savour of a timidity which is really inconsistent with a firm and well-intrusted faith.
Wilberforce spoke for about 30 minutes following Draper's presentation and his talk was likely a condensed version of his paper in the Quarterly Review. Darwin himself spoke favorably of Wilberforce's article. In a letter to Hooker he stated
I have just read the ‘Quarterly.’ It is uncommonly clever; it picks out with skill all the most conjectural parts, and brings forward well all the difficulties. It quizzes me quite splendidly. …
If indeed the traditional story about the debate is largely myth, why has it endured so long? The reason most often given is that there was a change taking place in the way science was done. At the beginning of the 19th century, as in previous centuries, science was not really a profession. It was more like a hobby for some of society's elite, many of whom were members of the clergy. By the 1860s there were a few young men, like Huxley, who were trained in science and wanted to make science a career. They resented amateurs like Wilberforce speaking out on matters of science. Thus, they saw that the story of Huxley getting the best of the famous Bishop could serve their ends of creating a closed scientific community where only those trained in science were welcome. Huxley himself had no love for the clergy and took every opportunity to diminish their role in science. In fact, later on he refused to believe that some members of the clergy actually accepted evolution. In the twenty years following the debate there was a changing of the guard in science, and science did become a legitimate profession. It was certainly beneficial to science to have scientists committed full-time to scientific inquiry. However, to exclude interested parties outside of science is not necessary or desirable. Thus, the quarrel with Wilberforce was not so much over what he said as with what he represented. To classify this event as a battle between science and religion is far to simple a view. For a more extensive treatment of the Huxley-Wilberforce debate I would recommend the papers by Lucas , Brooke , and Smith  as well as the article in the American Scientist .