To me, and also measurements, the HE-6 has more than neutral in the treble, which may make it sound bright. However, more power or current won't heal that, but people hear it as a little bright, and then assume that it is a lack in the amp. A weak amp with a source having a rolled off treble is a good tool to test my point. My HM-801 portable player demonstrated this.
I've heard these headphones on many, many different types of amps. One thing I've noticed is the treble and bass response change from amp to amp. Some lesser quality amps will spotlight the treble and weaken the bass. On higher quality amps the treble was tamed and the bass had weight. The amp I'm using now is a current driven amp with only 10watts into 8 ohms.
So for me. Mega watts and loads of power wasn't the answer. As I use to run these on 200wpc mono blocks. They sound better on the amp I'm using now. Smooth treble, Large soundstage, Deep tight bass, lots of body (full).
This has been my experience.