Let's be honest, there are already some big dogs in the park we're entering.
Should we be structuring this site around the expectation that people will go to Wilmott for X or NP for Y?
Those other sites will still serve a very important purpose: for discussions. This simply isn't permitted here, and those sites already do that well.
The primary difference is the platform and everything that comes along with it.
People should come here for answers to real questions. Whenever I go to those other sites I end up getting really frustrated as I waste time reading dribble from people who have no clue in order to get to the good material. Here, not only do good answers get pushed to the top and good users get rewarded, there is also a strong community (including moderators who understand this) which should serve to raise the bar on questions that don't meet a minimum level of quality (enforceable through the wiki nature of the site). Other forums simply can't compete with the software and community-structure.
In terms of the competition aspect of the question: IMO, if we provide a better service then we will win on that front. I could easily expect within the year for this site to be the first source for answers on quantitative finance. When StackOverflow started, it also had to compete against established sites.
Quant SE is for professional quants (as well as interested students and academics) to ask questions they actually face in their day-to-day work. We've been pretty vigilant about closing questions that fall outside this realm. And because this site is dedicated to Q&A, there are no discussions about the news, etc.
I assume your real question is:
How will QF.SE compete with NP and Wilmott?
Stack Exchange competes just fine against Experts Exchange, Quora, Yahoo Answers, Wiki Answers, etc. Part of what SE offers is a really elegant platform, to which only Quora comes close. But mostly it's because each SE site is focused on one task, so there are a lot fewer distractions.
I'm more than thrilled to see another quant community that I can learn from and participate in. We need more participants, more discussion, more Q&A, more blogs, more news in this niche. There are really not many resource in this field.
Each site does one thing well and everyone should be able to choose which site fits his personal taste to be a part of.