The few times I've sat down and perused the New Testament, I've been struck by the mythic feel of most of the stories. (Well, this applies to the Old Testament as well, but that's not my focus here.) In fact, in the parts that directly talk about Jesus, only the Semon on the Mount has a non-mythic feel. I suspect that, as in any mythology, many of the New Testament stories are borrowed from other cultures and mythologies. For example, a number of quotes are attributed to multiple historicoreligious figures, such as Jesus and Siddhartha Gautama. As mythic tales are passed down, they are applied to the receiving culture's heroes.
So many of the tales of the New Testament have little to do specifically with Christianity, and these same stories have an ageless, mythic quality to them. However, the Sermon on the Mount stands apart. It isan exposition, an analysis, a discussion of previous teachings. There are no action scenes to speak of, and it is highly philosophical. It has the feel of rhetoric, not story-telling. I suspect that it is far more historically accurate than the surrounding text -- it also has the feel of a belated transcription, like someone who was present at one of Jesus' speeches went home and wrote down what they remembered of it.
What I find intriguing about this explanation of the striking difference in style is that the Sermon on the Mount is also regarded as the core of Jesus' teachings. A number of non-Christians or non-standard Christians agree with the teachings in that particular story, but have doubts about the others. Some regard it as the true core of Christianity. (Perhaps the writing style is simply more believable, but could this not be due to the same logic I use here?) I don't have any particular position on its relationship with Christianity, but I do hold that of all the Jesus stories, it is the most likely to be historically accurate.