OK, OK, I have the 20mm f/2.8, and I just do not use it much anymore. I think it is sharp, but it must be about 5-10 years old. The 16-35mm f/4.0 VR is one of my favorites. Distortion is taken care of in LR 4.1 if I so desire. The other wide zoom is the 14-24mm f/2.8 at $2000 USD. Or for the same price the 24mm f/1.4 or f/3.5PC.
If one were to look at a 28mm f/1.8G, the latest prime from Nikon...this may be a great lens. And at about $700. However, the DXOmark scores for the Tokina look very good and the most likely difference may be in the build quality. As you noted the Tokina does not have a filter thread, but for $750 vs. $1150 for the Nikkor....
I will say this....at the ocean, I put my D4 with the 16-35mm into an Ewe Marine Housing, and the lens fits into a special ring which requires a thread on the front. So, if you have that in mind... and, all my lenses have a front filter to protect the element.
In conclusion, I love the 16-35mm lens. I use it for a walk-around. But I also am not up tight about distortion...my 10.5mm modified fisheye suggest this.. I think if used properly one gets excellent results from the 16mm end. If one points it up or down, sticks heads on the edge, or expects all the lines in a room to be straight when shot head on....
Unfortunately I do not have a D800, so my stuff is shot on a D4
Here is 20mm at f/4.0

3000px size http://www.flickr.com/photos/fantinesfotos/7699924890/sizes/o/in/photostream/
and one at 16mm, a panned shot with the car moving about 15 mph.

3000px size http://www.flickr.com/photos/fantinesfotos/7575448010/sizes/o/in/photostream/
If you go to my Flickr photostream, you will find some of folks on a beach...16mm not posted here because I want to live some more... but you can see the distortion is not so bad...
Hope this helps...