I listened extensively to the headphone output of the B60 integrated amp (the preamp of this unit is dreived from, and is supposed to be very similar to, the BP-20/BP-25).
The headphone output (derived from the preamp, not the amp) of the Bryston is actually very good in comparison to the headphone out of every other component (excluding dedicated headphone amps) I've ever heard. It is neutral, open and has more than enough gain to drive my Sennheiser HD 600s. It possesses good extension at the frequency extremes and has plenty of dynamic slam.
That said, my dedicated McCormack Micro Integrated Drive headphone amp easily bested the Bryston. It was more open still, more transparent, and it possessed better soundstaging abilities. Dynamically, the two units were about the same, but the greater transparency of the MID gave it the edge in portrayal of microdynamics and the presentation of detail. The MID was a little brighter than the Bryston, however.
If headphones are a secondary means of listening for you, then I think the Bryston will be more than sufficient. It does an excellent job. However, if you are assembling a headphones-only system, or if you intend to listen primarily to headphones, than I would think your money would be better spent on a dedicated headphone amp (Headroom, Sugden, Corda, etc for solid-state; RKV, Antique Sound Labs, Wheatfield, etc for tubes). Keep in mind that some of these headphone amps also function quite well as minimalist preamps (from what I've heard), but in this case, the tables will have turned; I imagine the Bryston would walk all over the headphone amps as a straight-up preamp.
Hope this helps!!