I may or may not wade into this conversation later because it is a massive question, but this question is pretty much the crux of modern day historiography in the aftermath of the "linguistic turn" of the 1960s, with the poststructuralists and the deconstruction of history as also a "text" rather than any collection of "facts".

The general consensus (with caveats) seems to be, when it comes to writing, the past is literary analysis. When it comes to archaeology, the past is very much a science. In so much as anything that we choose to write down is a science or a literary analysis, but that's a whole separate argument on the philosophy of science.

I think that's more of a personal opinion. My professors discuss it a lot and if they don't agree on it, I'm quite sure that it's not just a or b. It has been considered as part of literature until the 19th century, and it's still quite important because, as they say, most of your sources are transmitted through language and you have to deconstruct what is said. But nowadays historians use lots of scientific methods while doing research, because eg. DNA or statistics give you information that language simply can't. It just depends on what a certain historian finds important, when he did his research, which institution he's active at, the subject he focuses on, and so on. I'm writing my thesis using a rather scientific method, but I will still need literary sources, while many of my colleague students do it the other way round. As I said: even my professors have been discussing it for the past 30 years, there's no real answer (yet?). So, it's really just up to you.