I personally think it has to do with sound sig just as much as ability to drive. I've heard a Schiit Lyr 2 do a reasonably good job, and I've heard a different Lyr 2 sound terrible, so it clearly had to do with the tubes being used along with the associated gear in each system.
I have very mixed feelings about the HE6's. The craftsmanship, on my pair at least, is God awful considering the price. They do sound killer though through the right amp.