First I setup my 42" as a standard white umbrella. I had my 580EX flash set to 1/8 power for all shots. This was interesting, as they are all exposed similarly. The light stand to subject ratio was about the same for each shot. Here is the first shot:
For the 2nd shot I turned the umbrella around and removed the black cover, turning it into a shoot-through umbrella. Note that although the flash is effectively much closer, my exposure was the same. This is interesting to me - I see lots of talk about how much less efficient a shoot-through it, but at close range the fact that the light source is effectively closer means you really don't lose any light. This is useful for product shots, still life and baby photos. With baby shots, this is great, as you can get the umbrella much closer as a shoot through, and thus get softer shadows due to the larger apparent light size.
Finally, here is the new 32". I like the fact that it gives a more defined shadow. Not a huge difference, but nice to have a few options to play with. Note that I used a vase that is partially reflective so I could see the different reflections that the umbrellas make.
I can't say that I would use any of the combos if I were shooting something reflective, but it gives me an idea of what my catchlight is going to look like - without having to bore one of my sons to death.