Famously – or perhaps notoriously – Steven Jay Gould proposed that science and religion constituted non-overlapping magisteria. In my opinion, his claim was not plausible; but a similar claim regarding the sciences and the arts does stand up.
I want to focus here on the issues of self-expression and collaboration.
Individual and creative thinking plays an important role in science, but it involves a form of creativity which is far removed from the sort of creativity which applies in the arts. The latter is always associated with self-expression; whereas self-expression has no role to play in science.
So self-expression can be seen not only as a key demarcation criterion between the arts and the sciences but also as an indicator that these pursuits are opposites, incompatible, non-overlapping. It is a crucial part of the one, and plays no part in the other.
Collaboration, on the other hand, occurs in both the arts and the sciences. But it is an essential – and defining – feature only of the latter.
The vast majority of the greatest works of literature, music and the visual arts are attributable essentially to one man or woman. The artist draws, of course, on his or her teachers and the broader culture but in a real sense owns – as author or creator – the finished product.
Similar notions can apply even to necessarily collaborative arts like the cinema. Think of the director, Alfred Hitchcock. The best of the early films he made in England have the same winning combination of suspense, latent eroticism and humor as his American masterpieces even though he was working with entirely different people in a very different cultural context.
The arts are by their nature self-expressive, even if the expression is often, as in theatre, cinema, etc., group-based or, as in much medieval art for example, anonymous. But even in these cases, I would argue, the greater works will be more likely to bear the stamp of an individual genius or personality.
Science is just not like that. It is the antithesis of self-expression, and is all about building a common body of knowledge. To the extent that the individual's ideas are deemed to be important, to that extent the science is undeveloped and uncertain. As a science matures all traces of pioneering individual contributions are erased or at least merged into a greater, more complex and more subtle body of knowledge than any single mind could even begin to comprehend.
There was an interesting exchange a while ago on a comment thread at Rationally Speaking about the nature and the scope of science which has a bearing on this point. A German botanist working in Australia was arguing that science is concerned with everything empirical and is defined primarily in terms of its communal nature.
"... [I]t is not science if I personally figure out whether Craspedia species are apomictic. I have to share this information in a way that allows other humans to test it, reproduce it, and build on it, because science is a community effort. But then it would be science no matter how trivial the fact."
Though not everyone will see the collaborative side of science as a key defining feature – another commenter calls it "unusual" as a demarcation criterion – science has, in my opinion, an essentially communal, individual self-erasing nature. (It imposes self-effacement, as it were.)
This criterion also fits mathematics. You get untutored geniuses (like Ramanujan) but it's only when they are integrated into the mathematical community (as Ramanujan was, thanks to G.H. Hardy) that they become real mathematicians.