I think, as a writer, you see the big picture, and as an actor, you're thinking of all the minutiae, all the very small details.
I think the benefit of being a writer is that I'm looking for the subtext on the page, because all good writing has subtext. And as a writer, you look at the big scope of things, the big story, rather than just your individual story line, because I think it's important to know what you're in and how you fit into it.