The idea of the Lincoln-Douglas debates are deeply ingrained in the American psyche, but I think it's time to face up to the fact that that era of the debate has passed.
Instead, I wish the candidates would do a written debate. I don't just mean "Send them each a bunch of questions and publish both responses", I mean an interactive series of answers and rebuttals. Randomly choose half the questions to send to the one candidate first, half to the other. Set some word limit. (And if were up to me, I'd tell the candidates that it's a hard word limit; send me 600 words instead of 500 if you like, but I'll just cut you off mid-sentence...) Stop at two or three iterations. In the internet era, I'd give them as many hyperlinks as they wanted and not count them against their word count, and invite the candidates to continue after the official debate on their own websites, if they like, giving both of them the last word.
We'd probably learn a lot more. The problem with debates is that they provide abundant opportunities to fail with little chance to succeed, so candidates play it so safe that you or I could probably write the responses actually given in debates. The name of the game becomes saying as little as possible; not nothing of course, but as little as possible. Making it a written debate would tend to turn that around; you have all the time in the world to vet a response, so you could actually say something conclusive, and back it up with links and references.
Of course, this is all predicated on the false assumption that politicians want to educate us about them, rather than adopting emotional sales techniques that involve feeding as little information as possible while pushing as many emotional buttons as possible.