Burson's headphone amp is based on their discrete op-amp (a very linear, high-gain amplifier stage).
I have compared Burson's op-amps to several of the top-rated op-amps and without a doubt they sound way better than everything I have tried: AD843, OPA627, OPA2604, OPA2132 and several others I do not recall right now, including some rare mil-spec versions.
I installed Burson op-amps in my ASR Emmiter amp, they have transformed the amplifier. Bass definition, midrange timbre, treble delicacy, soundstaging, dynamics, you name it, the Burson Op-amps beat any IC op-amps I have tried, hands-down.
Few solid state heaphone amps are fullly discrete, so, extrapolating from my experience, I believe that you can not go wrong with the Burson discrete circuit approach.