Actually, these are best leveraged together---big data and powerful analytics have deep meaning when positioned in the context of powerful stories. Stories give people a context in which to position the analysis provided by the data.
This is a really nice article about how well data and stories work together.
The only piece I would add is this: share your stories first, and then support them with data. Most often people go for the data first, and then maybe share a story.
So do the reverse and you won't put people to sleep or have them looking at you with a quizzicle eye wondering, "And what does this data mean?"
Story is the meaning-making part of the equation. Data is the sense-making part.