From what I've read and seen the Sigma should be a bit sharper than the current Nikon 16mm Fisheye. But you have to find a good one, which is not easy.
I just got my third Sigma 15mm FE (all bought new!). The first one was really bad (soft), therefore I decided to exchange it against another one. This one was slightly better, but still not great. Even stopped down to f/11 the corners were soft and the contrast at every aperture was rather low. I thought that maybe the lens is just like this and kept this version.
After reading some more tests, where most people were really happy with the performance of their Sigma 15mm FE I decided to make another trial and ordered my third Sigma 15mm FE. It arrived two days ago and is signficantly sharper than the other two. I will now send the second one to Sigma to get it repaired (and keep the third one in addition).
Summary: If you buy Sigma lenses don't just trust the quality control of Sigma, instead test your lenses yourself. All testing was done with a D800E, which of course shows any lens problems immediately.
Regarding the Nikon Fisheyes: The old 3.5/16mm seems to be significantly better than the current f/2.8 version. I got one used in mint condition and it is really great. Sharp in the corners, even wide open. CA is comparable with the Sigma and the colors are much warmer than the Sigma (probably good for underwater use, but maybe a bit too warm for landscapes above water). I'm planning to do a test between these two lenses in the next couple of weeks (first above water and than later underwater). But of course the 3.5/16mm is not an AF lens which is a signfificant disadvantage underwater and the close focus capability is as bad as the current f/2.8 Nikon FE, meaning significantly less good than the Sigma.
If this test confirms my first impression I will probably use the old Nikon MF lens for half half shots with manual prefocus and for all other underwater situations use the Sigma.