The nikkor 10.5 has superior optics. It is a "fast" lens. Max aperutre is f2.8. It will shoot superb images at f2.8 to f8 apertures. It performs especially well at f2.8 which is rare in lenses. Why does this matter? because small apertures cause diffraction which = soft images. In low light or tuff interior shots you can open up the aperture without loosing sharpness. You can also pick a fast shutter speed with a large aperture to get even sharper images in low light.
It is also a full frame fisheye. This makes full use of your sensor. The lens does not have a full 180 across the verticle or horizontal. This gives the advantage of imaging a smaller part of the scene hence the 6 or 8 shots required. But the real advantage is it is easier to properly expose each frame because the lens is not having to "resolve" such a large area of light (areas of your scene). The dynamic range that the lens "sees" is much less than the sigma.
It has a huge depth of field and only requires focusing other than infinity when closer than 12 inches to objects.
Moving objects are more difficult to deal with when shooting 6 or 8 as opposed to only 4. Especially people. With the sigma you have more overlap per image giving you the ability to use layer tricks to blend back in the legs and parts or moving objects.
The Sigma 8mm is a very good lens but is considered a round fisheye and is not as "fast". It produces a cropped "drum" image which wastes part of the sensor area. However this lens will make excellant images and should not be considered inferior in any way.
'Techinically" these two lenses are not really comparable optically because they are totally different designs.
More images per scene always produces better quality when speaking in terms of "pixel data". But one must consider the photographers ability to make good use of the lens. This relates to "angular resolution". This very basically means the more pixels in your image the greater the detail is when displayed at larger sizes. For example you could create a "multi row" pano from more the 24 images using a longer focal length lens like a 35 mm. Because each frame is imageing a smaller part of the scene then the total of all the frames will make a very detailed image. However to make use of this amount of detail (pixels) your image will have to be large in dimensions and consequenlty large in megabytes. To see the detail you will have to zoom in. So doing it this way does not give you any advantage. But is shows the point.
To put it another way you are striving to create a sharp image displayed at a "normal" field of view. This means around 90 degrees. Your display window reflects this "field of view". So you want the image to be as sharp as possible without being zoomed in or too zoomed out. Imagine your filed of view as you stand in the center of a room and turn your head. Your display window"field of view" shold be close to this.
Much like in 2 or 3 shot with the FC-e9 lens shooting 3 gives better quality than shooting 2. The same thing applies when shooting 6 full frame fisheyes vs 4 drum.
I forgot to mention I use the Nikkor 10.5 and have a lot of experience using this lens.
Personally, I find it easier to get better exposures and manage dynamic range problems much easier using a full frame fisheye than using a circular fisheye.
It is not any harder to stitch 6 or 8 vs 4 drum providing you have properly leveled and rotated your camera.
It takes slightly longer to shoot a scene but this is relative to the difficulty. Most typical scenes can be shot just in 1 or 2 minutes.So timewise it is irrelevant.