The difference between the two styles has to do with whether you are trying to get someone to change their beliefs and/or behavior. I suggest that if you run an experiment, you'll find that even people who prefer to read in a factual style will be more likely to actually change their beliefs or behaviors when information is presented in story format.
(Heck, you might not have to run that experiment; ISTR that there's already a study showing people shift attitudes as a result of identifying with story characters.)
Eliezer is right: stories are better writing... IF your intention is to influence your reader.
So, if you don't care what your reader does with the information you give them, and you don't care if people who aren't already motivated to obtain that information get bored and tune you out, then feel free to simply provide facts. If you want people to care about the thing you're writing about, stories are a requirement.
tl;dr: facts are far, stories are near.
(ETA: the book Wired For Story has some background information on the science of brains and stories.)
For a long time, Eliezer has been telling me I should write more like he does. I've mostly resisted, preferring instead to write like this:
At the recent Effective Altruism Summit I tried to figure out which personal features predicted writing style preference.
One hypothesis was that people who read lots of fiction (like Eliezer) will tend to prefer Eliezer's story-like style, while those who read almost exclusively non-fiction (like me) will tend to prefer my "just gimme the facts" style. This hypothesis didn't hold up well on my non-scientific survey of ~10 LW-reading effective altruists.
Another hypothesis was that most people would prefer Eliezer's more exciting posts, while people trained in the sciences or analytic philosophy (which insist on clear organization, definitions, references to related work, etc.) would prefer my posts. This hypothesis fared a bit better, but not by much.
Another hypothesis was that people who had acquired an epiphany addiction would prefer Eliezer's style, whereas those who just want to learn everything efficiently would prefer my style. But I didn't test this.
Another hypothesis that occurs to me is that people with short attention spans could prefer my more skimmable style. But I haven't tested this.
Perhaps the community would like to propose some hypotheses, and test them with LW polling?