Diffusion or Softbox?
In achieving soft light is there any benefit to going the route of a softbox as opposed to simply clipping diffusion material to the front of the lights?
It depends on the look you are going for.
A softbox is going to be a fair bit softer and a lot more controllable. Clipping diffusion material to the front of a hardlight will soften it a bit, but usually the instrument will still give a hardish look. Sometimes that's the look you want. It's mostly because when you do that, you can't put nearly as big a piece of diffusion in front of the instrument as compared to the softbox face, and you can't put it as far away from the face of the instrument as it is in the box. Therefore, the softbox has a much bigger surface area that becomes the light source. Also, the softbox is all contained, and there is little to no ambient light spill. For even more direction, you can put grids or eggcrates on the face of the softbox to give the light more direction while still remaining soft.
I use softboxes a lot... but I also use white umbrellas a lot, especially in situations where I don't need the light "contained" and ambient spill is not an issue. I shoot the instrument through them, using translucent umbrellas (not the reflective kind). I'll usually go to umbrellas when, because of surrounding factors, an umbrella or a softbox would give me the same result. I mostly do that because I'm lazy... it takes a couple of minutes to set up a softbox from scratch, but about 5 seconds (literally) to pop up an umbrella. Most of our hardlights already have umbrella mounts built into the yoke so it's painfully easy. BUT, if light spill or controllability is an issue, I'll still choose a softbox.
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The advantage, if that's the right word of the softbox (as Todd also mentions) is in controlling the spill, especially with the easily applied louvers and eggcrates; but also the physics of the light bouncing around inside the box, which most often has silvered sides, intensifies both the amount of light and the softness or evenness, which is really measured by the softer shadow than when simply attaching diffusion to the doors.
Part of this effect is also because the size of the box is usually larger than door mounted diffusion. Of course another alternative I've often mentioned is using a large 4x4' or unrolled curtain of diffusion either alone in front of the light or even in front of the softbox (double diffusion!). In the situations that allow such a footprint, this is the most beautiful quality of light yet.
If you're trying to decrease the density of the shadows, scrim on the barn doors won't do much. Shadow density is related to the size of the source, and the distance from the subject. A large source, close to the subject, whether it's a softbox, a butterfly or a simple sheet of foamcore and a bounce light will produce a much softer, less dense shadow. The texture of the scrim has little to do with shadow density. And a piece of scrim cut to fit the barndoors, just doesn't significantly increase the size of the source. So the shadows will have the almost same relative density as the bare instrument, but the edges will be a little less pronounced.
You can see this effect at work in noting the difference in shadows between a sunny day and one with a high thin overcast. This is the small source far away, vs the large source close up. It's not the texture of the clouds that reduce the shadows, but the fact the entire sky has become the light source.
I have a system, it has stuff in it, and stuff hooked to it. I have a camera, it can record stuff. I read the manuals, and know how to use this stuff and lots of other stuff too.
You should be suitably impressed...