I'm sure the HD560s are great, but the issue is my listening preference. I EQ to the Harman target and then add a sub-bass boost (in form of a low shelf), which ends up at +10dB at ~25Hz. That leads to almost 20dB of boost at 20Hz, that the HD560s need to suit my tastes, which is unfortunate, considering its distortion at low frequencies. I bought the HE6se because of their strengths in that region.
Bass distortion is the worst, since at those frequencies, the audibility of the harmonics relative to the fundamental is the strongest, compared to any other frequency. In addition to that, music is not linear in spectrum, but more like pink noise, which means bass playback levels will be much louder than treble.
Considering theses issues, the HE400se has an estimated 15dB more clean headroom over the HD560s below 200Hz. The HE400se's distortion issues above that point only come out way past 100dB, which I will never reach at those frequencies.