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That's an interesting spec diff that I never noticed before. The thing that comes to mind for me is that the silver may be polished somewhat to make it more specular/efficient.
If that is the primary case of the differences (other than the obvious white/silver), and the shape of the BD appears to be the same, it could be akin to the difference between shining a light on a mirror vs. a piece of white paper. One (mirror) reflects the light much more narrowly iaw AI=AR, while the other (white paper) "scatters" the light into more directions due to the greater variance in surface texture (i.e. more angles).
I've got no experience with the PCB BD's themselves, but my silver BD is much more textured than the what the PCB offering appears to be in the web pics. I'd think that for most BD applications, the white would be the way to go, as the polished silver (vs. soft white or textured silver) would be pretty "hot". Of course, you can always "sock" it.
You might want to give PCB a call and discuss it with them, but for a first time @ BD, I think the question is more about a specular vs. diffuse lighting output ... people largely opting for a BD to provide softer wrap light with the center plate blocking (also removable) some of the direct light that can create hot spots. So, imo, unless you have a specific reason for going with the PCB silver, the white would be my recommendation for most people. I'm using my silver BD often as a large silver reflector in addition to a "BD".
I'm sure others can chime in with more direct experience between the two, but I do find the difference interesting. You might ask PCB if they have a link / file of an image showing the lighting pattern difference. Maybe they've got something that just isn't on the website. You can also check out the technical forum @ PCB where you could post a question on the issue.