It really depends. Naturally, Voldemort is cunning. If he wishes for the Cullens to accept him and his deatheaters he would plan ahead and sketch out everything before commanding his deatheaters. Many of the deatheaters have dabbled in politics and Voldemort himself has a very logical mind, suggesting he is fully capable of out-witting the Cullens by his persuasiveness. J.K Rowling herself had said Voldemort was based on Hitler, and we all know how persuasive Hitler's speeches are. She gave Voldemort many of Hitler's qualities. But on the other hand, we all know some of the deatheaters are moronic dumb-wits. And that without Voldemort guiding them, they're as good as idiots. I say the deatheaters would never hope to compare.
In conclusion, if Voldemort is involved (as in not communicating with the Cullens himself but instructing the deatheaters of what to say), the Cullens are bound to lose. However if it is only the deatheaters against Cullens, I'd be surprised if they triumph.

I'm very much undecided.
On the Cullen's side they can in milli-second of a flash kill all of them with a twist of their necks.
However the death eaters can say word and a twist of their wand and their all dead, regardless of them being 'dead' {No beating heart}

The words 'rational discussion' stopped me. Yes, both sides are very intelligent and cunning, but the Death Eaters have very short tempers, which could get them into trouble. I agree with @Helena that without Voldemort, they might lose, but of course they would have Severus Snape, and there are other intelligent Death Eaters. But the Cullens are very smart and persuasive too. In the end, it would depend on what they were discussing.

Purely because I don't believe that the Death Eaters would have a 'rational discussion'! They'd go straight for the kill and I hate to say it because I adore the Cullen's and what they stand for, but they'd get killed.

^I agree. But why would you say that the Cullens would get killed? The Death Eaters would. They were able to handle a bunch of newborns (with some help with the wolves). Newborns are stronger than Death Eaters. The Cullens have a bigger chance of winning.

The DeathEaters would either walk away, or just kill them.

The Cullen defenetely on all fronts. They would win on a debate, simply because the death eater's ideologies are so obviously flawed as well as reviled by the majority. The death eaters are also not the most composed lot. They get very emotional and loose control easily, specially around those with different views. And if the rational discussion failed and it degenerated into a fight, the Cullens would finally do the job for the order and wipe out the death eaters and leave Voldemort with no allies.

The Cullens, for the most part, are calm and logical, especially Carlisle. Unless their bloodlust gets the best of them, I don't see how they would lose an argument against Death Eaters, who, for (again) the most part, are pretty hot tempered and rather irriation, for lack of a better word. Death Eaters would rather lunge in for the kill than have discussions. But again, this is a generalization. Nonetheless, I can see the Cullens beating the Death Eaters in a debate of some sorts by their practice of patience.

Define, 'rational...' according to whose standard here?

Voldy is pretty manipulative and what not.