I think Bin Laden and his allies in their network "won" in that one goal was to make the west fear the abilities of their network to disrupt the west, and make the west paranoid that it was in a war it couldn't win.
However, as has happened before in history, antagonists from other cultures failed to understand the full dangers in attacking a powerful western nation. I would suspect that Bin Laden would not ultimately have wanted the increased US presence in the middle east even if such presence ended up causing more spite directed at the US. Bin Laden and his allies, with the stereotypical images they have of western and specifically American mindsets and behavioral parameters, would have trouble understanding that Americans would simultaneously lose their minds with fear and paranoia, yet enthusiastically sanction sending thousands more of their own citizens into harm's way. Westerners are characterized as weak, fat, arrogant, and fallen from righteousness with their foreign religions and sinful beliefs.
Of course, one thing I would think (pardon my ignorance if so) is that men from Bin Laden's culture would have trouble understanding as well the space between the average American citizen and its military. Yes, the US is very proud of its military and their image as the heroes of the world, but the vast majority of US citizens have never been in a service nor have any family members in a service, nor do they have any real experience with an unstable society or war being up close - until 9/11. A certain segment of Americans are quick to say "sic our troops on 'em and bomb up to hell, those godless heathens"; most of them have nothing personal to lose from the fighting. A person from a more troubled region of the world might naturally assume you'd dread having to send your citizens into a meat grinder where the long-term enemy has the advantage and can wage a bloody war of attrition and terror. Dread enough that you would not do it, especially if you'd just had your nose bloodied and told that "they" can get you any time they like, if you come where you're not wanted.
But, in simpler terms, Bin Laden and co. simply couldn't have understood the ignorance of some parts of America and how its media would just aid that ignorance and misunderstanding the goals of the attackers, too. From almost day one, the crazies have helped the ignorant see this as a stand-up war of justice that we gotta sally forth and win just like World War II. (Aka, the war America wants every war to be.)
