I don't subscribe to the notion that narrative or storygame mechanics inherently mean the game or campaign will have a better story than a game played with a more traditional RPG.
Depends on your definition of "story", I guess. You can certainly get satisfying stories from traditional mechanics. I still remember the Pathfinder game where I one-shotted* a dragon by getting a lucky triple-damage crit after using Smite Evil on it (with Smite Evil adding 3x your level to damage on the first attack against an evil fiend, undead, or dragon, so the attack did something like 3x(1d8+35)). That kind of thing is satisfying precisely because of its randomness and rarity.
But cold, hard numbers rarely cooperate with narrative arcs. They particularly don't cooperate well with "softer" values, unless those values are also given cold hard numbers (e.g. using Willpower as a metacurrency in various Storyteller games, or using relationships).
For example, let's say one party member is under the logn-term influence of an enemy telepath/illusionist, and has been made to see the the world as an antebellum plantation and the party as rebellious servants/slaves who need to be punished and slain, or at least brought to heel. Another party member has been in a long-term relationship with this character, and challenges the telepath to a psychic duel... which he, not being particularly good at that kind of thing, loses badly. When dealing with a "cold numbers" system, that's it. He lost, it's over, they're done.
But since the GM is running a more narrative system, the mind-controlled PC says "Hey, I just saw my lover brutally killed in the mindscape. Could I maybe get a new roll to resist and add our relationship strength?". The GM agrees, and she succeeds in breaking free of the control, and turn the tables on her erstwhile master and his allies. That's the kind of thing you generally don't see in a more traditional RPG.
* Technically, the dragon was somewhat wounded from a previous encounter in which we drove it off, but still.