The Beyerdynamic DT931 is one of the most underrated headphones by folks in these parts.
I haven't heard the stuff you listed, but maybe I can compare it to other things that might be familiar to you.
Compared to the 501, the 931 has less detail and less air. With the Headroom Max (the one I compared the two on briefly), the 501 sounded thin with shallow bass to me. It sounded a lot like other headphones sound when they are underpowered (imagine the Sennheiser through a headphone jack). The 931 was,, in my opinion, much better suited to the Max and sounded full and complete.
The Sennheiser HD600 is like a sister headphone to the DT931. They're over the same class and sound similar in some ways. Major differences include the DT931's having very forward vocals compared the the HD600's somewhat recessed vocals. The DT931 is not as warm as the HD600 but seemed to be more "realistic" in its frequency response (it's hard to use the word flat when they're both nowhere near flat). With the Headroom Max and Melos SHA-1, the HD600's bass was sloppy compared to the tightly managed DT931. The HD600 did, however, have slightly deeper bass extension and the sloppiness of the HD600's bass yielded a more "full" sounding bass that many people prefer. This also caused the HD600 bass to be slightly more tactile.
In my experience, the HD600 benefitted greatly from using a larger amp. The bass tightened up and became really nice with the RKV. I never had the luxury of listening to the DT931 on the RKV amp. I imagined that it would pair nicely but still not have the bass extension of the HD600 and still have more forward vocals (something I feel the HD600 is in need of, but perhaps not as much as the 931 has).
Hope this helps.