Sorry but that depends on the headphone amp and speaker amp in question, it's not a gimme.
I have heard a number of typical amps from Rotal, Nad, Cambridge Audio, Yamaha, Marantz etc up to £600 and none have been better than my Master-6 driving the HE-6's.
I fully expect better speaker amps to be better with the HE6, if synergy is good, but to say that the HE-6's are going to sound better just because it's being used on a speaker amp is just wrong.
Yes I agree. I have heard that the HE-6 does sound well with some headphone amps. But the point I was trying to make was that most headphone amps lack the power requirements needed.