I have not tried either of the two, but I did have extensive experience with BCD-1, BDA-1, BP26, and a whole range of amplifiers, as well as Squeezebox and other similar products, and Squeezebox had very poor performance, what made me build my own PC based transport and not even consider Squeezebox or other products available at the time.
It is all about the engineering and execution, and knowing those other Bryston products I am willing to bet that BDP-1 would offer better performance. As far as looks, features, functionality goes, cannot comment.