I bought the HD560S right when they came out, to see how it would compare to my HD6XX. I also own Hifiman Sundara, and for closed-back listening I have AKG K371 and DCA Aeon 2 Noire. They all have their differences when it comes to stock sound signature, but after adjusting each to my liking with EQ, the HD560S is easily my favorite for daily use. It is light and comfortable, with a simple durable design, providing great value in all respects. The main benefits I found over the HD6XX are: 1. enhanced spatial qualities, 2. more space for my ears in the cups, and 3. the single connector (vs both sides) is more convenient.
As far as EQ for the HD560S, I started off with Oratory1990's EQ, since it seemed to make an improvement, then I made some additional modifications based on resonances I heard during A/B testing of pink noise. In general, I also agree with Solderdude that extra attenuation of the upper range helps to take the 'edge' off. This ended up overcomplicating the filter set a bit, and the improvements may be specific to my own ears, but you can see the resulting curve below.
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One thing that I discovered while tuning EQ for the HD560S is that my ears aren't perfectly symmetrical, as we would all like to believe they are. Using a
tone generator, I found several frequencies where one side dominated the other, the main one being a 5 dB peak at 4500 Hz on the right side. To confirm that it wasn't due to L/R driver variation, I performed the same test on the HD6XX. The peak was not as high, and at a slightly lower frequency, but it persisted even after turning the headphones around. For the HD560S, I believe the angled drivers and the extra space given to the ears increases the effect on frequency response of any differences in driver to ear interaction between the two ears. I fixed the differences between my ears with additional notch filters on the individual L/R channels. The result was a much smoother sound. I have since done similar tuning with my other headphones and found smaller, but still noticeable differences between my ears. I especially recommend to any HD560S owners interested in EQ, that you check and correct for any L/R resonances, as the result may have as much of an effect on your listening experiences as overall EQ for tonality.