The Sigma F4 EX DG 8mm Fisheye was replaced by the superior Sigma f/3.5 EX DG 8mm Fisheye quite some time ago now.
It really is not fair to compare apples with oranges.
Based on your camera....
The Sigma 8mm Fisheye is a circular fisheye and can cover a full 360x180 in 4 shots (*Drum) where as the Nikkor 10.5mm Fisheye is a full frame fisheye 180 degree diagonal and requires 8 shots to cover the full 360x180.
Yes, the Nikkor 10.5mm Fisheye will be somewhat better than the Sigma 8mm Fisheye in clarity and resolution but simply because it is a different style of lens and requires more shots.
If you do want to compare apples with apples you should be asking about the Nikkor 10.5mm, Tokina 10-17mm Zoom and the Sigma 10mm fisheye lenses all of which require 8 shots (6+TB) full frame at their widest settings.
The Sigma f3.5 8mm Fisheye is a better option for moving objects simply because it requires less shots to cover the full 360x180.
*Drum = A side cropped full circular image because of the 1.5x multiplying factor of the small sensor of the Nikon D50 DSLR. Reducing the width of the circular image by cropping of the side edges and reducing view from 180 degrees to around 140 degrees horizontal whilst retaining close to 180 degrees vertically when the camera is in portrait shooting orientation.