Not that many headphones that are better than the 560S at any price if you ask me.
Hello.
I've owned the 560S for over 7 months (based on a review on audiosciencereview and bought them) and listened to them for several hours every day (with arturia minifuse 1). For its ~$150 in Europe or the US, this is fantastic sound. A couple of weeks ago I bought myself HD660S2 and now I will never go back to cheaper headphones no matter how praised they are. The difference in price is huge, these are different classes of devices and cannot be equated with each other. I'm an ordinary person without musical education or music production skills - but even for me the difference is very significant. When I compared them directly, I was surprised how I thought the sound of the 560S was so pure, but now, in comparison with the HD660S2, their frequency response (560S) seemed to be drawn by a 3-year-old child, and there is a small layer of cotton wool between the emitter and my ears).
I'm not sure if moving to the next level (another 2-3 times higher price) is worth the increase in quality that will be obtained. I think the next level is around the Audeze MM-500 (maybe 820S or 800S2?), but can the average person appreciate their sound quality? This is already an ultra professional technique (or you have very large pockets)
I use HD660S2 with Topping DX5. I'm sure that the DX3 is absolutely suitable as an amplifier and I wanted it, but I didn't want to use a Jack->mini jack adapter
The only reason I didn't choose the HD650 is because these headphones were created using technology that is 15 years old. (Partly for this reason I ignored the HD660S, as well as the minimal price difference with the S2 version + slightly increased bass on the S2 - this is very, very cool for open-back headphones). That's why I chose the HD660S2, because logically: today it's like the HD650 in 2009, which will be recommended even in 15 years
P.S. I listen to both models (listened) with the original oratory1990 equalizer
P.S.2 Pay attention to the weight. When I listen to 560S/660S2 - they are weightless and 3-4-5 hours without a break is not a problem for them. But when I put my Focal Bathys on, I want to take them off after 30 minutes because of their weight. So Senheisers are very good only because of their light weight (almost half the weight of other models) and convenience
P.S.3 I listen to all genres of music (except for extremes: super hard rock or tech house consisting of 2 sounds for all 6 minutes of the track)
I hope I was useful to you. I will be happy to answer additional questions. PM questions