The idea for the book apparently arose after a dinner the two men attended, and so they decided to down lances and amicably write about their fears, their literary loves, their philosophical predilections, and their fathers (more on fathers than mothers). It's a little bit contrived, but so are these two writers, both of whom live their lives very much always in the context of their public personas. It should be remembered that in France Houellebecq, at least, is hated by many; his progress in the Anglosphere I think has been a bit smoother. As for Levy, he's got money and is also an intellectual; perfect fodder for critique right there, I suppose.
As for where they sit on the ideological spectrum, I suspect that Houellebecq's pronouncements make him suspect-looking from either side. Levy probably is of the left, but not in it. Contradictory characters, it seems.
Houellebecq's hang-dog demeanour in the book lets him hide, however, an advantage. In the end, he comes out of the contretemps looking like the stronger writer; there's just something a bit too glamorous and steely about Levy for my taste, something adopted as a pose in view of the planned publication of the correspondence. Houellebecq seems to be the more subtle thinker, also. But these are probably not important considerations. From my point of view the most important thing going into this book was to understand better one of my favourite authors. Now, to get a better handle on Levy I have ordered a couple of his books. To orient myself. To better understand.