The best format seems to be an opportunity for both sides to present their case. No debate. Debates place the two sides on equal footing, automatically giving the nonscience side an undeserved upward boost. While the science side will present cogent arguments and evidence, the nonscience side will boost their appeal with speculation, nontruths, stories or even lies. But, they can easily be persuasive with charm, humor, emotion or propaganda. It's not a fair fight because the rules for each side are not understood to be the same. Scientists are used to logical arguments. You can't win an argument with someone who is not being logical.

Because debates are meant to persuade to one side or the other, it is not always clear who wins. People tend to favor the advocate of the idea they preferred when they came in.

I was going to add a comment to idoubtit's answer, but I'll run out of space. So this is also a response to Brian Gregory's comment above.

A public debate is not the best forum for a detailed, reasoned argument over an issue. No one pauses a debate in the middle to look up a reference or confirm a statistic. A well informed, well reasoned scientist will lose to a charismatic, funny, ignorant believer. Often the minds of people are not changed, but I don't think they are necessarily reinforced a great deal - people walk in with an opinion they feel justified in, and unless they hear something that really shakes that belief then they walk out with much the same opinion, whether their proponent wins of loses the debate.

But, and this is very contingent on the audience and location of the debate, there may be some people who do not have a strong opinion one way or the other. These people may be influenced, at the very least to think some more and/or do some research. And much like advertising relies on repeated exposure to sell a need and brand a product, then repeated exposure to challenging thoughts may lead to these people forming a reasoned position. Conversely, repeated exposure to debates conducted in strongly biased forums, where the rational position is not given a proper hearing, work against science.

So, although a debate isn't the best forum, we do still need to engage the BS spinners and their arguments actively in public forums, and this probably includes some debates. Scientists have done a lot of sitting in their academic enclaves talking only to each other over the past decade or two while the ignorant and credulous have had the public's ear, and that has contributed to the current state of public ignorance.

So looking specifically at debates the question must be is it worth engaging the woo spinner, and the answer is specific to the case. For a given debate, we should ask: Can we offer a good debater on the side of reason? Is the direct or indirect audience going to include anyone who may be swayed? Is the moderation going to be fair? Is there going to be any form of editing that may skew the outcome and distort the discussion? So we must conclude that some debates will be worth engaging in, others would just be propaganda fodder for the credulous.

Perhaps more importantly, is the question of what is the best overall strategy to counter the crap. Debates may be necessary, even helpful in some cases, but they can't be the only tactic when dealing with proponents of the fallacious. We must engage them in other forums, educate and train ourselves to be better proponents of reason and science, and fit it all into a big picture approach to improving the scientific literacy and critical thinking skills of society at large.

I enjoyed the Hitchen & Fry vs. Widdecombe & Onaiyekan, but really only watched it to see what Fry would say. I've seen a number of True Believer vs. Skeptic / Atheist / Scientist / etc, and nearly without exception they come off as little more than a waste of time.

Believer walks up to the podium and makes glaringly incorrect assertions about the world around us, about science in general, and about their opponent's position.

Skeptic is forced into a position of refuting the Believer's assertions rather than making his own points.

Believer ignores corrections, and points out how science is often wrong, and then makes some other wildly innacurate statements.

It typically ends up as a back and forth of misstatement, correction, ignoring the correction, and misstating... round and round.

To even enter into a debate on the existence of God or the efficacy of Homeopathy gives the Believer and their fans a sense of validation - that science is finally giving them a chance. It may seem crazy, but I can't think of a case where Ray Comfort or Jenny McCarthy has walked away from a "debate" and done anything other than claim wholesale victory or at best blame the other side for highjacking the debate.

The Believers will ALWAYS claim the victory.

I think no if you are talking about formal debate with a moderator and those trimmings. I say yes to informal water cooler debates in a respectful down to earth way. I like to goto paranormal meeting and interact with believers and not all skeptics are arm chair skeptics. I don't believe everyone is suited to this but I love http://www.joenickell.com/ approach to skepticism.