I've been playing around with UWA (Sigma 10-20) and fisheyes (Rokinon 8mm and DA 10-17). The question I was trying to answer is whether a fisheye could successfully be de-fished to provide a satisfactory rectilinear perspective. Yes, I know, a fisheye is a fisheye, and its primary purpose should be for those 'whimsical' fisheye perspectives. Still, a lens like the DA 10-17 FE is a remarkably small lens compared to the Sigma 10-20, and at 15-17mm it is quite nearly rectilinear and easily de-fished.
HERE is the thread with my results.
When it comes to wide angle lenses, this is the conclusion I reached, but perhaps others can confirm whether or not it is true:
An UWA lens can be physically designed (i.e., hardware) to render a rectilinear perspective OR nearly the same thing can be accomplished with a fisheye lens via software in processing.
That is, a rectilinear UWA lens is going to have its own set of compromises and distortions to get things rectilinear. A fisheye doesn't have to deal with those things in the same way. In many instances, defishing and cropping a fisheye shot can provide a more natural perspective than a rectilinear UWA. Again, there will be compromises, but I found that even after cropping, a 12mm shot on the DA 10-17 provided the same angle of view as 10mm on the Sigma 10-20.