The softness of a light is determined by the SIZE of the source (the source in this case is the bounce or diffusion frame, not the light hitting them) relative to the SIZE of the subject, which is affected by the distance to the subject. That's it. A bounced light or a diffused light isn't inherently softer or harder compared to each other, it's all about how large an area of soft light they create, and ideally how even that light is from edge to edge. So if you bounce a light off of shiny white board and get a hard kick off of it, or you spot the light into the center of the bounce surface, you won't get as soft a light coming from that bounce compared to a flatter, more even light hitting a matte white surface where the light fills the bounce surface evenly. Same goes for shining a light through a diffusion frame, the softness is determined by the size of the diffusion frame and how evenly the light fills that frame with no hot spots, no unevenness of brightness, etc.
When I mean by the softness is determined by the size relative to the size of the subject, or the subject's distance to the soft source, is that if you are the subject and from your perspective, a 6'x6' soft light takes up the same size in your field of vision as a 12'x12' soft light that is twice as far away does, then the softness of the light would be the same in both cases, the only difference would be the speed of the fall-off in exposure -- if the soft light is much closer to the subject, then it falls off in intensity much more quickly as the subject moves away from the light compared to a larger but farther soft light, where if the subject moves a little closer or farther towards the soft light, there would be a milder change in exposure.
So in theory, once you evenly fill a soft source, bounce or diffusion, from corner to corner, the light cannot get any softer. If you fill a 6'x6' frame of Full Grid Cloth evenly from corner to corner with no hot spots, then the light won't get any softer if you doubled the thickness of the Full Grid Cloth because the size is determining the softness.
What a book light does is allow you to fill a diffusion frame more evenly by using a bounced light to fill it, and you therefore get as much softness as is possible by filling the diffusion frame as much as possible with no hot spots.
Now in practical reality, some people might find it easier to fill a soft white beadboard as a bounce than shining a light through a diffusion frame, depending on the material.
Sometimes which way you go is a space issue, do you have more room for the light that hits the card or diffusion from behind or in front?
Also, soft light is not some monolithic effect, if it is not a theoretically perfect and evenly bounced light or evenly-filled diffusion frame, it will have some hardness or texture depending on the nature of the inefficiency. For example, let's say you use a silk as a diffusion. It spreads the light in a sort of X-shape pattern instead of a circular glow. The weave of the fabric may also be loose enough that besides spreading the light, it also allows some sharp light to leak through the holes in the fabric, creating a soft source with a fainter hard source mixed in. If you bounce a light off of a shinier surface, you may get a hot kick that also creates a fainter hard light in the center of a larger soft light. Some people like these effects, the faint hard light mixed into the soft light can create some feeling of sharpness, some interesting specular kicks off of reflective objects, etc.