I think people find the separation of the Stack Exchange network a little complicated. On Quora, you can make a new topic in seconds. On Stack Exchange opening up a newer area of discussion isn't so instant.
But yes, Stack Exchange sites easily beat Quora in the quality of answers where Stack Exchange has an established site, it's just that Quora has a wider range of topics.
You talk like Stack Overflow and it's sister sites don't exist!
No, it's just that I don't think of Stack Overflow (and sister sites) as filling the same niche as Quora. I mean, yeah, OK, they do "compete" to some extent, sure. But at least in my mind, I go to SO and SE sites for different kinds of discussions than what I go to Quora for.
I'm happy that SO / SE sites are more Open Web friendly, but that doesn't mean I wouldn't like to see a site, styled after Quora, that is so as well.
But yes, Stack Exchange sites easily beat Quora in the quality of answers where Stack Exchange has an established site, it's just that Quora has a wider range of topics.