I was just thinking, there's really only 2 kinds of game to play. You're either in a sandbox setting, where you can wander all about & do things wherever/whenever you want...or you're being railroaded into following the pre-set storyline & strung along like a rabbit following a carrot.
Seems like you're either making you're own story (sandbox) or following a story that's told for you (railroad). Some folks prefer their freedom, while others like to know what they're expected to do next.
So which do you prefer and why?

Both. Depends on the game. Obviously RPG's benefit most from some sandboxing however Batman:AA didn't suffer from being a railroaded adventure.

I'm not a fan of either extreme. If I have all choice and no pre-set story, then the environment seems shallow in some ways. (To me.) On the other hand, if the game is all preset, with no decision making, then I feel as though I'm just along for the ride, and there is FAR less re-playability.
I prefer to have a mainly scripted storyline with plenty of choices and options. This way, I get a superbly crafted storyline, far more intricate than my choices could have forged, AND yet I still have plenty of freedom where it makes sense, and will actually add to my experience.
Sorry, but I just don't either of the extremes. However, if you really want me to choose, then I'll say scripted, as I've played plenty of scripted RPGs and they were still fine.

Eh, I'm not sure I follow. Sandbox games follow just as much a pre-set storyline as a non-sandbox game, unless the storyline is nonlinear (which we can pretty much completely rule out these days). The only difference is the progression of movement.
Some games also manage to find an OK middleground between the two, like, for example, several semi-open interconnected areas.

Somewhere in the middle, I think... would that be a railbox or a sandroad?
I mean, there ARE games with multiple possible stories that cross each other every once in a while and finally end up at largely the same place, no?

It would be a giant sand monster made of sand,railroads, and boxes.

/\
As he said.
Take Oblivion for example. Most people will claim it's sandbox, and yet, all quests in the game are fairly linear. But The Witcher, while being more restrained in the movement part, is pretty awesome in the choices departure.

Depends on the game, both can be good.
If its a linear game, then the storyline and gameplay better be really good, and the scripted events impressive. Choice isn't necessary, but it doesn't hurt to give players multiple ways to approaching the same linearly arrived at situation.
If its a sandbox game, then my actions better have some sort of impact on the gameplay world. If I can do small meaningless things everywhere then there's no point. If I can do whatever I want, and those things affect other things, then its cool. But even sandboxes require some direction.

The OP's preference seems clear, at least...

I don't know how anyone can argue sandbox games are non-linear. GTA railroads you through the plot as much as any game. I think sandboxes are good at offering the illusion of freedom. You can wander around all you want but in terms of actually effecting the plot nothing you do really matters. Whereas a good RPG will offer you real choices which is probably as close to non-linear as we're going to get.

The issue with Sandbox games for me is that games become really short on the Story mode.
You can finish Saboteur in less than 6 hourse if you skip all the other stuff the blow up and destroy which makes it nearly 60 hours gameplay. Yes, Saboteur is THAT big.
Or another anoying thing is looking for certain stuff you have to collect to get a 100% of game. And if the game is glitchy it just doesn't make fun. I remember Spyro 1 where I couldn't get past a certain gape because of a glitch. Or Psychonauts last level. Meh.
However, it always depens how you work out the game. Zelda: OoT is the prime example how Sandbox games should be.
Linear games are also good, don't get me wrong, but I always like the mix of both,especially if they are involving Plattformer and Action.

I'm actually not entirely sold on one over the other. I do like being able to wander around and explore, but I also don't want so much freedom that I have no idea where to find something of value (if its an adventure game) or something that won't utterly destroy me (if its a combat-based game).
This helps alot too. I kinda feel like most of the stories to be forceably told (linear/railroad) have already been done in some capacity, whereas sandbox lets me decide more on the story I'm taking part in.
I think I like a sandbox that has at least a few carrots in it. ;-)

I prefer SandRoad.
Not too open that you get lost, and not too railroaded that you can't even walk 5m out from the path.

A sandbox with several railroads in it.

19th century America?