I guess I shouldn't have worded it as "what is better?" rather "what's your preference?". I understand there are really good variations of both, and some of the best even employ a bit of both.

Does anyone think that an effective story can be told using a full non-linear game, given the state of technology and the amount of storage available for such?

I feel immersion can also be broken with too much freedom because the product can lack polish or compelling content because it's shoehorned into do whatever you want. A lot of characters and storylines will be available, but very few are ever fleshed out. This is why I'm not a big fan of non-linear personally. The story and characters get shoved aside for the sake of choices that usually don't really affect anything anyways.

In theory, I think both types of games are equal overall. In practice, I think linear games are much more superior to non-linear games.

While I agree that the story tends to suffer on a non-linear game, there are examples where some nonlinearity can assist in the storyline. Take for example FF6, where you can choose from the three groups making it to Narshe. Character development however, I think does not get affected by nonlinearity, especially when the nonlinearity involves different characters. Once again, FF6 with Locke's story, Cyan's nightmares, Strago's childhood, etc. The majority of the second half of the game os entirely nonlinear, yet involves a LOT of character development.

both have their place

Whichever you are in the mood for and happens to be well made

I prefer Linear for the fact that story is generally more of the focus.

I guess a question like this seems to be pitting storyline against challenge/gameplay, which I'd consider to be the two most important aspects in a game. Has anyone got any examples where effective speedruns/self-made challenges can be made on a linear game, or a nonlinear game with a storyline like a linear game? I'd love to make a game of the latter description, despite how much time it would take to accomplish such a thing.

Both and neither. You can have great games of both types and crap games of both types, so it comes down to personal preference.

I prefer a mix of both. I often like the "levels" or the overall progress of the game to be linear, but I like those levels to give me enough freedom to make up my own strategies without being so open that I get lost or distracted. The Halo games are a perfect balance of linear and non linear. The missions follow a logical path so the story can be focused and compelling, but the combat can be handled who you see fit and thanks to the best AI in gaming it's never exactly the same.

So in that regard I like Zelda the way it is. In Zelda OoT you almost always needed one thing to be able to do another. Some times the game would just plan tell you that you had to do something before you could do anything else. But, at least with Zelda, it's not the order of the dungeons that matters so long as the overall progress though the story has a beginning, a middle and an end.