First place I'd look would be Language Log. There's nothing right up top right now, but if you look around in there you will find some informed comments, informed, at least, in the sense that they know quite a bit about human languages. If you look around through their links something more to the point may show up and it's a good trip just all by itself. The general opinion that I've seen from those pages is that the big difference is that human languages use recursion. Dig around some more and you'll find posts that explicitly address the question of animal communication systems. Apparently there are some that do use recursion, but we, as humans, have not spent a lot of time examining that particular question. Whether because we have rejected the possibility out of hand or not I couldn't say.