I have the 10-20mm (on a D300) and my brother has a Nikon 12-24mm that I borrow from time to time.
The Nikon probably has slightly better corner sharpness, less chromatic aberration, and perhaps maybe slightly better distortion control. None of these are really that important where wide angle shots are involved, to be honest. Your shot should distract someone from getting a magnifying glass and inspecting the top left corner of the photograph.
Nikon certainly have the edge on build quality and quality control, but I don't mind the build quality of my Sigma at all. I've heard that some 10-20mm lenses have very poor corner quality, but most retailers will swap the lens out for you, or you could make use of the distance selling act. For what it's worth, I've used the sigma in the rain, I've chucked it loose into a bag, it feels very very solid.
Even though I have access to both, I almost always use the 10-20mm. I'm not alone here, Thom Hogan does the same:
http://bythom.com/sigma10to20.htm
Basically, I have a wide angle lens to go wide. My 10-20mm rarely goes narrower than 14 mm, and spends most of it's time at 10mm. I've grown to love the distortion (but I can remove it in DXO if I want.)
Click the image to go to the flickr page where you can see the data/enlarged versions.