I'm not really sure how to answer, because I find it enjoyable to play both purely tactical/stategic games as well as those that are nearly purely storytelling.
However, I find "story" to be a poorly defined term here...
See, I don't think D&D is a
story game (nor are most rpgs). This is
not to say that stories don't happen within D&D, but stories also can happen when playing the sportsball. "Story" is how we humans make sense of the world, so whatever happens in the game, we can tell a story about it. While traditional rpgs like D&D provide a mechanical basis for deriving an imagined narrative, most do very little at all (mechanically) to create a "story" with a defined beginning, middle, and end. When it does happen, its either the result of a skilled DM "landing" his D&D ship well, a not-so-skilled DM fudging rolls or railroading, or random chance.
That's, I believe, the root of the "conflict" inherent in the G0-G6 ratings to which some of the other posters have objected. That is, mechanics and story don't have to be in opposition. For example, the creation of a (complete, but not great) story is necessary to even have the game
Once Upon a Time function, similarly with
Fiasco. And yet, within D&D and most traditional rpgs, the idea of mechanics being in conflict with the story is completely sensible to me. As far as I can tell, the preservation of story vs the mechanics is the sole reason to "fudge" die rolls. I don't see how "fudging" a card in Once Upon a Time or a scene in Fiasco is even possible, let alone necessary to preserve a story. This becomes particularly egregious, IME, for rpgs that try to address episodic properties like Star Trek with D&D-like mechanics. (Seriously, at the very least, games like that should have some kind of "escalation die" thing where you're stumbling around in the first act, okay in the second act, and rocking it for the third act to get things resolved.)
What most rpgs like D&D
do provide is a framework upon which to string a
narrative or explore a setting in a uniquely visceral way because we identify with our avatars in the gameworld. And honestly, that seems like plenty for most folks (me included, most of the time). YMMV, and all that. So, I don't intend what I wrote above as a sweeping indictment traditional rpgs, just an assessment. (Except for the Star Trek and similar property rpgs...those are all horrible
.)