I A/B them with my Hugo direct and Hugo via EF6 and to me HE6 sounded better in both setup but the gap increased when amped by the EF6 and hence my comment HE6 will scale better with more power. They are more similar sounding than different to me so it's not really a preference of say preferring LCD3 over HE6 or vice versa but to me HE6 is superior in sound while HE560 is easier to drive and have better comfort. For those who have the upstream to amp the HE6, it would be a downgrade to move to HE560. But for others HE560 make a lot of sense.
My 2 cents...
How would you describe the soundstage compared to the HE-6 ?