This is what the OpenGL_options page on the wiki says:
Doom: A close approximation to the software renderer's display. Uses GLSL to handle the increased brightness around the player's viewpoint; otherwise identical to "dark".
Software: Uses GLSL to replicate vanilla Doom's light diminishing algorithms, including the increased brightness around the player's viewpoint. Falls back to "dark" if shaders are unavailable.
These both sound like a roundabout way of saying the same thing. So I want to ask, what exactly is the difference? It seems that Software causes a stronger difference in lighting over distance, and allows the banding to be switched on.
I have some more things to say, but am keen to hear if I'm just being a dork
"Software" very closely replicates the actual original Doom lighting equation.
"Doom" was an early attempt at doing such, before the EDGE algorithm was ripped. As of now, though, "Software" uses the same algorithm that ZDoom uses, which is also later what the truecolor software renderer uses, too.
"Software" should give you the closest possible lighting method to the original Doom experience.
Perhaps it would be a good idea to rename some of the lighting modes (if not cull outdated ones), because what's there is very confusing. If you want the lighting to be like vanilla, would you pick Doom, Standard, Legacy, Software...? Going by name alone, any of those could refer to the vanilla Doom lighting model (where "Legacy" is interpreted as the legacy Carmack renderer, rather than the Doom Legacy port if that's even what it implies). What's worse, since the mode has a drastic effect on the brightness/visibility of the maps, various mods expect different modes because that's just what the modder thought was right and other ones will make it too bright or dark.
Culling outdated modes, as well as clarifying which are are most like (and least like) the software renderer(s), could go a long way to help with that, since they will at least know to mention if they're not using the default vanilla-like one.
The main issue with 'Software' is that it requires shaders. Back when the other formulas were implemented, even top of the line hardware was not capable of lighting an entire scene using shaders. That's where "Doom" comes from. It was the closest I could get with the available features. The modes were just never renamed later.