First off, this link may interest you: http://www.quora.com...redirected_qid=35617
Can't spot an equivalent question on StackOverflow although I'm not registered.
Design-wise based on the FAQ, StackOverflow is not a discussion board.
Quora is also not a discussion board but it has a very discussion board feel. Not only because subjective questions are allowed but the design is more suited for discussions ala Facebook.
Quora might gain more initial members because as most techies may hate but general users may love, Quora not only connects to Twitter and Facebook by default but they use it to make your friends find you easier.
Quora's incentive is also based on LinkedIn's reputation-like profile and it also borrows heavily from Twitter's follow button (although this is just an illusion for a feed, it adds to the "feel") while StackOverFlow is more of a technical Slashdot/Reddit/traditional rating system although heavily improved upon.
Feature-wise, the core contention is design.
Quora as of right now uses a very unique notification/feed system based off of a combination of many services.
StackOverFlow is more of a tag-based traditionally well designed Q&A model.
In that sense, StackOverFlow has a problem in that it's much closer to Ask MetaFilter but doesn't have that community.
Quora is not only much quicker at adding questions but much quicker at encouraging answers. It's almost like a professional social game built around real questions only it dodges the Yahoo Answers problem both by having a smaller developing community before going public but also because it has no "public" overview page and therefore it's not about just discovering questions but rather it's a combination of auto-discovering questions tailored for your interest like with the way Twitter works (although this sounds much more appealing than it works)
Simply put, the reason the design goes beyond design and is a feature for Quora and not for StackOverFlow is that Stack is all about Ask and Answer. Quora is all about Add, Add, Add. (whether it be question or answer)
Finally neither is really for general knowledge nor a sure fire situation yet because of the instability of Q&A models in itself.
Quora just gets more hype right now because it's a very next generation Wiki besides having the hype of former Facebook members.
Generally, although this isn't the accepted universal definition, Web 3.0 is taking Web 2.0 Ajax sites and instead of creating services, it maximizes filtration.
In this sense Quora's model right now is the first Wiki that feels more like a post editor than a Wiki and it works surprisingly well currently which is why it's like magic before the model gets abused (and it is abusable)
StackOverFlow's biggest problem for general knowledge is that it isn't real time. Much less aggressive at notification. Much less encouraging of edited answers. May be too much of a well designed but classic take of Q&A sites and while that in itself isn't bad for power users, Quora gets "it" more that half of the battle of Q&A is inspiring participation and interaction while StackOverFlow sticks to improving a old model that generally doesn't stray very far from an already existing competitor in MetaFilter.
It's core design advantage though is that like MetaFilter and Yahoo Answers and WikiAnswers and Answerbag, etc. etc. - it's much easier to view and search for questions in a traditional manner. That same model though doesn't translate to generating increased participation of members on the site.
I.E. if I type SQL, I get a Google-like search box style page minus suggestions. If I type SQL in Quora, I may get a poorer view because there's no text box but rather an auto-real time updating suggestion pop-up down box. (Think typing in FARR)
Quora solves this issue though by having tags that are just as much keywords ala Facebook which serves as the "search result page" equivalent of StackOverflow.
Bottomline though, StackOverFlow's system if used generally is going to be much easier to share in public because like many listings such as Delicious, Stack is just a big tagged list of questions.
This doesn't quite work this way though because Quora understands and is banking on long tail Google search as the way to discover Quora answers.
That is, they don't put enough faith that someone is going to treat Q&A site like Delicious.com where I type Delicious.com to skip Google's poorer results.
They are banking someone is going to type a search on Google and because of Quora's high signal vs. noise answers, the page appears without someone searching on Quora itself.
To off-set the sharing problem and short term searching of things to answer, Quora relies heavily on member only features.
This means you'll have a hard time searching for a big list of questions currently but if your question has been asked before WHILE you created the question as a member, it can be re-directed.
Similarly instead of wondering what questions you know the answer to, just follow a topic you want and Quora will show a feed of the recent combo of questions containing your interests while using a notification system to alert you if someone adds an answer, comments on your answer, etc. etc.
It's feel is slightly synonymous to Twitter but it actually works better because the system is much closer to Reddit if you ever participated in that service as a member (I dubbed the system the red message box of ingenuity - Reddit's that is) although the system is also quite different.
The problem with Quora as a general knowledge base though is that in Quora's desire to adhere to signal over noise, they tend to under-estimate how many users will feel bothered by someone editing their post.
In StackOverFlow's system, your question is yours but on a public page.
In Quora just like in most Wikis, your question and answer is still yours theoretically but it feels like someone else's because people WILL edit your post and it can be discontenting until you realize, so far no one is abusing it. The question remains though whether it can scale through abuse.