Thanks. It turns out my hearing isn't good enough to actually perceive any differences between the two.
So far, EQ'd to oratory with a bass shelf, I'm enjoying these. Definitely too bass-shy for my taste in stock. It's hard for me to quickly do AB comparisons, but I think they do sound more spacious than the HD650, K371 and Denon D7000. Still not quite speaker-like in presentation. In terms of bass, I think my closed cans have a more subwoofer-like presentation, however, with a +6dB low-shelf the bass of the HD560s is very satisfying and full-sounding to me. I am pleased with this purchase for the price I paid. Without the ability to PEQ, I think I would not keep these though.
In the future, I'm still interested in trying some higher-tier planars.