Here is a comparison from DIY-Audio-Heaven.
HD599.
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HD560s.
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I read gooh things about the soundstage of the HD560s, but they score worse than the HD599 over Rtings, and the HD599 are mediocre at best at soundstage, as Rtings reflects.
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Over Amazon.es HD599s are at 106,56€ at the moment and HD560s are at 149€.
Let me know if you see anything in the data that justifies those additional 42,44€ (33.2% increase).
Also, HD599s are at 50 Ohms and 106dBSPL. Whereas 560s are at 120 Ohms and 110dBSPL. I don't know if the European Apple dongle is enough to move the 560s, but it is enough, I can assure you so, to move the HD599s.