From a design perspective, I think that there are two valuable questions to ask when you're making a game. (Well, there are about a zillion, but for this discussion, I'm interested in two of them.)
1) How important is the story?
This is one of those questions that generates a ton of opinions, but for which there isn't a flat right or wrong question -- unless you gauge by the marketplace. Some players really want a sandbox in which they can play around for fifty hours without ever going after the main storyline. Some players want a movie in which they play the fight scenes, and everything else is narrated for them. Some players want a really solid and involved story from which they can deviate into minor stuff whenever they want.
Oblivion joins games like the Grand Theft Auto series in saying to the player, "There's a story if you want it. It's not the world's best story, but it's there. Really, though, this is a sandbox. Go out and have fun."
Jade Empire and Neverwinter Nights 2, on the other hand, are firmly in story-land. You can break away from the story to do subplots, but even those subplots are usually tied into the overall plot in some way, and there's little of the sandbox feeling. Those games are made with story in mind, not exploration.
Neverwinter Nights, by contrast, tries to walk the middle ground. It had a story, albeit one aimed at a multiplayer experience, but it also had a lot of exploration, and you could just wander and find a dungeon full of bad guys without a whole lot of relation to the main storyline. Rogue Galaxy does some of the same stuff -- the game is linear for the first 20 hours, but the spawn system means that you can wander around and practice fighting moves and upgrade your equipment as long as you like. The story will always be waiting for you when you're ready to move along.
2) What tools are you willing to use to convey the story?
BioWare and Obsidian both rely heavily on interactive dialogue. The player feels like there's some control over the conversation, and often there IS, but there are also a lot of conversations in which, one way or the other, the player is getting put onto the story rail to learn the next plot point.
JRPGs don't even bother with the handwaved illusion of choice. The player gets cutscenes... a lot of 'em.
Beyond conversation and cutscenes, tools I've seen used to convey story in different games include:
- Ambient lines. Some action games actually get across important plot details just by what the bad guy is shouting during the big fights.
- NPC reactions. If selling the holy elven dagger to the orc barbarians causes all the elves to attack you on sight, you don't need a long cutscene or follower explanation to explain that selling that dagger is going to make the elves hurt you. Simple AI scripting can take the place of conversations or cutscenes here.
- Art. One of the things I liked in Jade Empire was returning to the school and seeing the damage that had been wrought. I don't normally notice art, but this was a time when a picture really was worth a thousand words. (There was also a cutscene, as well as some dialogue with a follower, but the art was what stood out for me most.)
All of these are valuable tools for storytelling. The key is figuring out how to use 'em, where to use 'em, and how MUCH to use 'em. I'm not sure that choosing your tools wisely will win over a player who wanted a sandbox game when you're specifically making a story-centric game, but I DO know that choosing your tools POORLY will piss off a player who would otherwise have been on board with the game you wanted to make.
I've been in meetings on projects where cutscenes are hugely important and major and big and awesome. I've been in meetings on projects where designers have a stated goal of avoiding you-lose-camera-control cutscenes for the entirety of the game. I think that you can make good games with either strategy -- different people will like those games, of course, but that's the fun of individual tastes. It's simply a matter of figuring out the right tools for the story you want to tell, and then using those tools properly.