I'm surprised to see the vast majority side with storyteller. Unsurprisingly then, I see myself as a writer. While the storytelling aspect is a given, and basically a necessity, I also find it the least interesting. While the idea that there are no new ideas is reductive and essentially wrong because of that, there is some truth to it. There are only a few plots, only a few twists, and I find myself most compelled as a reader (and driven as an author) by the process of making it new. It isn't that the STORY hasn't been done this way before, but that something along the way has been changed, tweaked, done better (hopefully), etc. that makes it new.
Granted, I also write strange, experimental literature, so...