The Daily Grind: Sandbox or story?

Jonathan Steinhauer over at WarCry.com has been working on a series of articles, 'The Death Of Story', and in the latest piece he explores variant methods of storytelling in MMOs. It's clear that there has to be a balance struck between, at the one extreme, story that is entirely handed down by the game in which the players participate (but which they don't direct) and at the other extreme, an open 'sandbox' where the important storylines are entirely created by players from the resources the game provides.

There's an increasing trend towards giving players tools to create their own stories. The player-built cities in Age of Conan come to mind, as does Eve Online's open-ended approach and of course the eagerly anticipated City of Heroes mission architect feature.

We're curious to know which end of the spectrum players prefer. Do you enjoy games where the story is predominant, expressed and played out through locations, quests and NPCs, adding to immersion but detracting from individual impact on the world? Or do you prefer a more sandbox-like approach, with the players' own interactions and creations providing the stories, and the campaign world in the background? What additional tools would you want to see, beyond city building, base building, mission creation, and the like?