I have no doubts about good speaker amplifier sounding better than headphone amplifier with the HE-6 but driven with Master 11 the HE-6 already outclasses many other TOTL headphones. I really haven't heard a pair of headphones that would make me sell my HE-6. If I could afford it I would certainly get different headphones to complement the HE-6 but none would replace it.
I have HE6 for a shot period with 6 mods (all the best recommended mods including direct hard cabling without connectors at the headphone end and grill removed). I ran it via Violectric V281 and V850, V281 is not a speaker amp but a almost the most powerful SS amp for all types of headphones (German made). I checked with a very long term HE6 user who had many amps including V281, Neo 430 and keep a Power amps only for HE6 and in his view you would not miss much with HE6 +V281.
I did like HE6 a lot and more than LCD2, K712, HD800, Elear and HE560. But now I got HE1000. I know HE6 has more punch but HE6 for me no where as musical as HE1000. HE6 laid back and punchy and very good sonic characteristics but HE1000 has everything but mostly- MUSICAL MUSICAL and MUSICAL.
I know lot of people here in HE6 thread says it is more punchy etc then why not use speakers themselves if that is the main driver?