Well that was fast... http://6moons.com/audioreviews/burson9/1.html Review is up!
Review states more bloom than the 160 - I think this amplifier should be very warm then seeing as I found the 160 already more warm in the midbass than neutral. I don't want to put words in Srajan's mouth but from the sound of the review he found the EF-6 to be warmer or smoother in the upper midrange and treble which are the frequencies responsible for the perception of "attack" or "leading edge" of transients. For those who find the HE-6 to be too incisive I'm pretty sure the EF-6 would be a better choice. For me though I think the HE-6 is essentially smooth in the upper midrange and treble, and just needs an absence of grain or harshness from the playback system to sound good and therefore does not require coloration to avoid fatigue. I unfortunately no longer have the EF-6 to qualify the degree of midbass bloom, but I do not recall having the impression of bass bloom like I got from the 160, but again my memory could be failing and I have not compared them side by side.
I think the issue of gain between the amplifiers is a bit misleading when trying to appraise power output. The EF-6 has 0 dB gain as default switchable to +10 dB and on 0 gain I never got past 12 O'clock. If the Soloist has different gain it is pointless to compare the output level especially not as an indication of reserve power. As you say for non-hearing-damage levels the HE-6 requires very little power, however I would speculate that given the differences between the HE-6 and most ordinary headphones, the fairly modest power supply may not be able to maintain as flat voltage as other more over-engineered designs, especially with questionable wall power quality etc. Still I guess you could always replace the capacitors with something more beefy.