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I just counted the number of projections available in PtAssembler and came up with 25. Some of those 25 are probably just there just to say that it's there and are not actually useful. Plus, there are probably a bunch that are so close to each other that in the real world it doesn't matter which one you use.
So let's say that there are ~10 usefully different projections. a) which ones are they? b) in what circumstances is one clearly better to use?
The PTAssembler link below explains a lot about those projections. It specifically answers the question you asked ... Why use the different projects?
http://www.tawbaware.com/projections.htm
Actually, as you'll see, PTAssembler has those variations so that you can get the control you want. Think of it as, what a DSLR is to a Point-and-Shoot.
Max Lyons added many of those variants when he wrote some of his code to replace some of Dersch's PanoTools. I use the Squeezed and Compressed Rectilinear variants for good effect.
V/R
B. Shaw
Which projections are useful to you depends a lot on what type of panoramas you're making, the image itself, and how you want to present the pano. That list is pretty standard for any Panorama Tools-based GUI (that's where the PT in PTGui, PTAssembler, PTLens, etc. comes from).
I'd say take a spin through this Hugin manual page on projections to get a visual sense of what each of them does. It's typically about emphasizing or de-emphasizing areas of the resulting panorama, because of the distortion that's required to map the larger angles of view or a spherical field to a flat plane.
As a 360°x180° panorama shooter, my needs are probably quite different from yours, but I tend to use equirectangular as the final stitching format, because it can encompass a spherical view (as cylindrical cannot), and stereographic for little planet remapping.
No panorama projection is usefull unless you need it.
So my question is, What do you need the panorama for?
I use some panoramas as:
Here is a paper I wrote some time ago as an explanation to a 3D modeling comunity, to understand a little more about the projections.
http://www.otake.com.mx/Apuntes/Imagen/EnviromentMaps/
I don't use some projections like mercator. In my opinion this are used to see the exterior projection of a sphere. A panorama is the view from the inside. The projections can be the same but the aplications probably don't.
And there other projections that I don't use as panoramas like rectilinear projection, but as normal photos.
