The HD800s is a whole other beast compared to the HD560s. Its really hard to compare but i think the HD800s is a bit brighter and cleaner but not in a bad way. They are colder and has less amount of bass but it has way more texture in the bass.

To do some kind of analogy i think the HD560s is like a really really good sounding studio.

The HD800s is like a top level concert hall.

To be honest i dont own the HD800s. I have the HD800 with SDR mod. Which i think sounds better than HD800s.

The HD800 you can, with some time an patience get quite "cheap" second hand and then just SDR mod it. I got my HD800 for 500€ second hand, but barley used. Lucky you might say and yes ofc but i also spent many many months looking and talking to ppl to find a great deal.