I'm sure James will be along with the definitive answer shortly...
But I'll chime in anyways -- From the looks of it, the output stages of the BDA-1 are very similar (if not functionally identical) to those found in the PB-25/26. (they are wired up a little differently though) And it is OK to use the balanced and unbalanced outputs from that device (so long as the input impedance is nice and high -- the BP25/26 has a *much* beefier power supply and higher rail voltage sitting behind these output stages as compared to the BDA-1).
This said, I have an HHB-CDR-850 and a BDA-1 (and a BP25) and I'm pretty sure that if you record the analog outputs of the BDA-1 using the HHB, anything you hear on that recording will be the A-D converters in the HHB, and not as a result of anything from the BDA-1. The HHB is a very good unit, and until I got my BDA-1, that was what I was using as a DAC. But, in addition to supporting more inputs, the BDA-1 sounds noticeably better than the HHB -- and the HHB is one of the better sounding units out there.
The other thing of note concerning the BDA-1 is that it actually has 4 dacs in it (well 2 stereo dacs) when using the balanced outputs, the "positive" and "negative" halfs of the balanced out for a given channel are generated by 2 of those 4 dacs. My understanding (and James, please correct me if I'm mistaken) is that this is intended to cancel out noise or errors from the dacs -- so the sound from the BDA-1 will be better when using the balanced outputs as compared to the unbalanced. Now whether any actual human beings could discern the difference in a blind test, personally I really doubt (I think we're talking about a small handful of db here, down around -130 or so).
--Ian.
