Looking first at DxOMark just to see what the lab reports say, the 28mm prime is seen to be twice as sharp as the 28-300mm (both measured on the Nikon D800 body) which doesn't come as so much of a surprise but the 28-300mm on a stand alone basis doesn't score terribly well on sharpness which did surprise me a little because as I have already noted, I've always been happy with the performance in this respect. Of course, this is also an average across the lens's capability in respect of its zoom range.
The test picture below has two areas circled, first in the centre, which is where focus was set. At f/4 on 28mm, the depth of field should see everything in focus across the frame. The second circled area is on the edge of the frame and will pose a greater challenge for the lenses.
In conclusion, the result is what you would expect and hope: a dedicated prime lens costing almost £500 outperforms the massively ranged 28-300mm which costs only 32% more. I would have been amazed had it been otherwise. The question in reality was always likely to be about how far the zoom would lag the prime on image quality - I think the outcome is a fair one.
The choice you have to make then is whether you need/want the highest quality image edge to edge, or whether the broader flexibility offered by a zoom better suits you. Knowing what I now know, I think I will in future be feeling guilty leaving home with the 28-300mm on the camera unless I really do need that flexibility (and sometimes I do). Mostly, as a quality obsessive and someone who examines pictures at 100%, I think going forward I will want to have the primes on my camera and simply change lenses when I need to. But that's just me.
In a future post, I'll compare the 300mm end with Nikon's pro 200-400mm lens and Sigma's 300mm f2/8.