I guess the big question is, what is it you do on your coticule? I would think you would do a dulicut coming from a 4K level hone, right? if you use only water I think going to your BBW would be adventagious otherwise not so much.

The general consensus is that a BBW is not realy usefull if you also have a yellow coticule. It would be usefull if your favorite yellow coticule is becomming realy thin, than you could decide to use a BBW for most of the work and only finish on your favorite yellow

a BBW has fewer garnets and those garnets are a bit bigger on average the those of your yellow coti. the main thing you need to acomplish is to get out the 1K and 4K scratches, after which al of those stone could be usefull finishers depending on your taste, aperantly even the BBW finish can be shaved with