Spectra and Dyneema are trade names. Both are HMPE, which comes in different grades. You can do a search on any of these and find gobs of information and products.
BCY and Brownell have different methods of manufacturing the materials into bow string--I believe this includes heat, stretch, number of fibers in a strand, etc., so it can make a difference, although probably not much of a difference for most. Several string materials also incorporate other materials such as Vectran.
Some here probably remember PENN-66 and B-75. Those were both dacron (polyester), but manufactured differently than B-500 or B-50.
The only way to know for sure what's going to work best for you is experiment. Some bows seem to "like" one material over another. Different strand counts, different silencer materials, silencer placement, nock fit, brace height, etc. etc. etc. can all make a difference.
Ray at BCY has always been helpful when I've had any questions--shoot him an e-mail and he'll address your questions better than I can.
Chad