Storytelling or Mechanics?

[Ramrodd]

      I think story should ALWAYS be upheld as the most important element of a tabletop. Simply put, it's why the players (and the GM) are there to begin with, to play an awesome story. Now, as far as the importance of mechanics, I think it depends, not only on the players, but on what type of system you are using. If you're playing D&D (particularly D&D4e) then the mechanics are important, because they're there for you to follow, and, in my experience, typically make things easier to follow, especially when deciding the outcome of events. However, when you get other, more open systems like GURPS or Cortex, the mechanics can be played with a little more openly, and rules can handle being bent, and it will usually come out better, as long as it makes sense in the story.
    Either way, i think the most important thing is that everyone at the table has fun, whatever that means about the rules and story. 

[frankfrak]

In my opinion the mechanics are very important at the beginning of the game, especially character creation, and as the game progresses mechanics are almost replaced by the experience of what your characters can and can't do. So by the point that people get familiar with their characters story should be the important thing.

[Hakuro de Killer]

In my opinion, story is much more crucial in a tabletop game than game mechanics. I mean yeah, game mechanics are important too, but one must realize that, the simpler the game mechanics are for a non-veteran D&D player, the easier it is for them to completely immerse themselves in the world that the DM has created for them and, in turn, allows those very same players to actually not only figure out what they can do at any given moment within the restrictions of gameplay, but also have spare attention span/brain capacity to actually think up the more asthetic aspects of a character, such as personality, appearance, and a backstory to explain it all and more.

Because take the story out of the game and you're effectively playing an RPG: Roll Playing Game rather than an RPG: Role Playing Game.

That's not to say game mechanics aren't important. Stats and dice are definitely necessary. But if you care more about a +5 Flaming Vorpal Greatsword of Shocking Grasp to go along with your +4 Adamantine Breastplate of Greater Sonic Shield than you do about the journey you went on to get such items, the NPCs you met along the way, and possible character development that would have actually made your character express some sense of individuality, that's clearly showing that your character is essentially nothing more than what's on his character sheet: A bunch of +'s, -'s, numbers, skills, and gear that, by the end of the session, are all but meaningless and essentially bland to someone who doesn't share your rather specific enthusiasm with game mechanics. On the flip side, a much weaker character that actually chose to develop plot and story would seem a lot more interesting to a lot more people. Also, by the end of the session, your character would have a full-fledged story that you could feel proud about writing and being a part of writing. I know that I would have a sense of accomplishment.

That's my two cents.