Have the HD600, DT880, K701 - had both the SRH840 and SRH940.
SRH940 defintiely gives you more upper end detail, is very quick - but lighter on the bass side - and build quality is very questionable (long term) ..... hinge cracking. I personally didn't like them - but can see why others would.
SRH840 is actually reasonably similar to HD600 - slightly more forward mids, and a touch more sparkle - but bass isn't as good (can be a little boomy at times), and has nowhere near the timbre, soundstage, or spatial presence that the HD600 has.
DT880 is a great phone - quite flat, very slight elevation in bass and treble - mids appear to take slight background step. Good at imaging. Can be a bit dry/lifeless at times. I found a tube amp helps. Definitely more detail.
My personal pick would be Q701/K701/K702. Very good soundstage and imaging. A lot of detail. Bass is there - but not the focus - less than the HD600 (no mid-bass hump). Very fast. Mids and highs more forward. Very good (IMO) with classical, acoustic, folk and jazz.
Hope that helps.