Of course, developing biases without testing them is bad science, so I decided to go through one year of neuroscience articles (from June 2010 to now; labeled as "neuroscience" by the journal), and see what trends there were. I made a spreadsheet containing each article, the date published, and a general categorization of the article (these categorizations are rough, especially for some "transdisciplinary" papers, and for papers outside my expertise, like developmental neuroscience). So what are the findings?
Nature publishes more neuroscience articles. Over the last year, Science published 52 articles tagged "neuroscience," of which twelve were cognitive neuroscience articles. In comparison, Nature published 73 articles tagged "neuroscience," of which only three I categorized as cognitive. Without getting into a discussion about the semantics of cognitive science, neuroscience, and psychology, if you work in a non-human system, you may want to try Nature first. (I am, of course, ignoring the huge issue of how many papers each journal publishes, total across fields, which may also explain this.)
Science publishes more speculative/non-traditional/hard to categorize articles. For example, "Human Tears Contain a Chemosignal," or "Astrocytes Control Breathing Through pH-Dependent Release of ATP." In general, I had a much harder time figuring out what to label Science articles. While I don't doubt the veracity of these articles, if you are truly pushing the envelopes in terms of interdisciplinary work, Science may be a better target.
Regarding subject area, Science skews cognitive, while Nature skews towards systems and translational neuroscience. As mentioned above, Science published twelve cognitive science articles compared to Nature's three. In terms of translational neuroscience (ignoring things like addiction models), Science published three translational articles versus Nature's twelve. And in terms of systems neuroscience, over 1/3rd of all Nature's neuroscience articles were in systems Neuroscience versus 20% of Science. Of Nature's systems articles, there was a slight bias towards vision (twelve articles).
Finally, what about birdsong in Nature? In the past year, there's only been one birdsong paper, from the Fee lab. Since January 2006, there have been eleven birdsong papers in Nature, about two per year. Of those eleven, though, six came out between December 2007 and December 2008 when I got the impression that Nature
As a systems neuroscientist working in olfaction and taste, the conclusions seem pretty clear. Try Nature first, unless I've got a good cognitive hook to the data.