Dawkins prefers his own argument based on the improbability of God (which he explains in the video we're discussing at 13mins 45 secs to 14 min 40sec)
I think Dawkins may have underestimated the power of the problem of evil. Given that the problem of good (see "The God of Eth" link, left) does indeed more or less conclusively establish that there's no all-powerful, all-evil God, why doesn't the problem of evil more or less conclusively establish there's no all-powerful, all-good God?
I'd suggest my "God of Eth" challenge sharpens the problem by exposing the rather laughable character of the explanations theists come up with to account for the sheer quantity of suffering that exists. Sharpened in this way, the problem of evil is, I think, pretty much insuperable for the theist. Indeed, I think it reveals that belief in the God of traditional theism is pretty obviously false.
Certainly, if we're focusing on what will actually change minds and win converts, I suspect the "God of Eth" challenge is rather more likely to give the faithful a jolt (so they may get a glimpse, if only for a second, of just how silly their belief system really is - I have already seen it induce a moment of wide-eyed panic in one or two: a real "Oh shit!" moment).
I think there may be potentially serious problems for Dawkins' appeal to God's improbability, which I'll come to next.