Maybe I shouldn't post at 6 AM anymore.
I didn't mean that a fun game inherently has no story, or that it is only one or the other, I should have made the poll question be is the game more about having fun or telling a story. If everybody is having fun although the plot is flimsy, versus everybody is bored and frustrated but it has this complex and intricate story that is unfolding.
In this argument, the "Story" proponent was firmly arguing that the end goal of the game is for the GM to tell a Story, and that's what is most important (in other words, if the PC's had a miserable time and the system was clunky, it's still a success if the GM likes the story he told). I was arguing that the end goal is to have fun, story may be a part of that, like there is a plot in any movie, but if you aren't having fun, there is no point for the story.
He was using as an example of his ideal game a WoD game he ran, where he scripted out the entire story well in advance, kept the PC's as mortals with no special powers but had lots of elder vampires, high ranked werewolves, and master mages around (so that their powers could prevent the PC's from doing anything that ran contrary to the story, and making sure that the PC's weren't key players in the story so they could not make any decisions that would not go along with the story), and considered the game a success because he told the story he wanted to tell, the PC's didn't mess it up and sat there and listened to it, and he felt satisfied. As a player in that game, I can say that it was a huge railroad game, it was pretty boring (breathless, long-winded descriptions of even minor events and throwaway NPC's, repeatedly roleplaying out trivial encounters, long scenes where he plays several NPC's that are having a discussion, or otherwise interacting), and if you told him you weren't having fun, he made it clear that you were there to watch his story unfold as he performed, and walking out on the game in the middle because you were bored week after week and weren't having fun would be like walking out of a movie before the climax.
I would use as an example of an ideal game my last D&D campaign, especially early on. I had 5 of my friends come up to me over the course of about a week and say they wanted me to run a D&D game, so we all got together one night and worked on making a campaign. We discussed what campaign setting we were interested in using, the general tone of the campaign, and then discussed house rules and what books we would be letting in, until I came to a consensus with my players about the system (D&D 3.5), setting (Forgotten Realms), tone (lighthearted with occasional serious moments, mostly action and dungeon crawls with some politics), and house rules. Once we'd agreed on the game, we played once a week, the players had fun roleplaying their characters and going on adventures every week, sometimes wandering from city to city, sometimes blasting their way through a dragon's lair or a kobold nest, and a larger overarching plotline slowly starting to weave many of their prior adventures into a coherent story. If the PC's weren't having fun, I wasn't doing my job, and if anybody wasn't having fun to please tell me so we can fix it.