cgardner
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Diffusion is a function of how many directions light comes from, and its varying intensities, relative to the objects creating the shadows. The same source can be made more or less diffuse by simply varying its distance.
If you compare size per the length of the diagonal, the length of the supporting ribs, the same size circle will always have more area and more point of light originating from greater angles. But whether or not the added size of the circle vs square or rectangle will make a difference or not really depends on how close to the subject it can be placed.
For H&S work either would work similarly, but as the light is moved further way the effect of the shape, assuming both are the same size as measured above, will begin to manifest itself. As a light source is moved further away the physical depth and light pattern spread become significant variable. Size and distance being equal a deep SB will project a narrower pattern of light than a shallow, resulting in different intensity and feathering characteristics.
What you also need to understand to meet your objective of "narrow pool, and wrap-around, at the same time" is how to make key and fill work together to create the illusion of "softness" and "wrap".
Softness is an illusion created by a number of perceptual variables: how the key light defines shape via placement, how light/dark and evenly the fill make the core area of the key light shadows, and the number of directions the light comes from (both key light size and direction the fill comes from).
Try this perception experiment. Set up a short lit oblique pose with a med. SB with the key light 45 from the center of the nose, or about 90 degrees from the camera axis. Put the fill light directly above the camera:
Start with the fill light off. Then without changing anything else simply gradually increase the amount of neutral fill in 1/2 stop increments until it overpowers the key light and the lighting becomes flat. What that experiment will demonstrate is the important role fill plays in the perception of "soft" in lighting. As more fill is added two things happen physically: the core area of the shadows get lighter and the front-to-back vector of the fill, added to the sideways vector of the key light in the transition zone at the edge of the shadow created by the key light, makes the shadow transitions smoother, i.e. the perceptual illusion of "wrapping" of the light.
Why that happens is explained by the physics. You think in terms of there being two separate light sources, but from the POV of the object the light is hitting its really just one source of varying intensities. So when you separate key and fill apart by 90 degrees, which is what occurs in a short-lit oblique view, you are actually creating a single huge feathered "virtual" softbox the size of the distance between the two lights.
But if the fill gets moved past 90 degrees from the key light, i.e. over two the shadow side, what happens is that the two light source vectors begin to fight each other.
Neutral fill "pushes" the shadow transitions of the key light backwards making them more gradual; like a car on the freeway colliding with one entering the highway from the side from an entrance ramp on the right. After such a collision where to the cars wind up? Pushed back and to the left.
When fill and key light cross the effect on the shadow transitions of the key light become more like a head on crash. The two cars meet and stop in the middle and wind up getting compressed and shortened. The further opposite the fill is placed from the key light the more the fill kills the subtle transitions in the edges of the key light shadows.
A way to achieve your goal of a "narrow pool, and wrap-around, at the same time" is to use a small but diffuse, non-specular modifier on the key light close to the subject to create the "narrow pool" and then simply dial in sufficient fill from the camera axis to make the shadows lighter and the transitions more gradual, the "wrap" component. Then to nuance the modeling on the shadow side add a reflector. With neutral fill doing the "heavy" lifting of the shadows the reflector can be wielded with precision, bouncing either the fill source, the key light, or a combination of both.
So the tool you need isn't necessarily a huge modifier for the key light, simply a better understanding of how to use fill effectively 
Chuck
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