If you're still wondering... I swapped emails with the PJB team a few years ago asking this same question. They told me same preamp, different power amp, in a nutshell. you *might* hear a difference, but it's a very small detail that wouldn't prevent me from buying whichever had a better price tag.
I have owned the D-1000 and the BP-800. The BP-800 power amp sounds more in focus, and cleaner. The D-1000 has a bit more presence of 1k-3k Hz, which I think helps the upright and acoustic instruments cut/speak, while making the 800 sound warmer or more natural. I think this is the generational advance of CLass D amplifiers- dialing in the natural sound and eliminating the extra bite of the high mids that characterizes most Class D tones.
I also own the BP-400 which looks and sounds more like the D-1000 than the BP-800; so I doubt there's much audible difference between the D-400 and BP-400 at all.