So here is my comparison for headphones I own, vs the SRH940. These are my opinions, and are by no means intended as absolute statements.
For comparison, all listening was done via a Fiio E9/E7 Combo. Music genres were broad spectrum, and by no means critical.
vs LCD-2 - The LCD-2 wins on Bass and Soundstage. The mids are surprising close, and I ever so slightly prefer the highs on the SRH940. I should note I prefer a brighter top end. Overall the LCD-2 has more impact, and crosses over into a broader spectrum of music, and seems to do everything well. The SRH940 also seems to have a bit of a hole in the mid-bass, that dramatically reduces it's impact.
vs. HD800 - In spirit, these are more closely alligned than I would have thought, but for soundstage and presence, the HD800 can not be matched. Sound signature is very close, with an edge to the SRH940 in female vocal, but male vocal goes to the HD800. The SRH940 sound stage is very good for a closed can, but if you are looking for a wide pallette, it's not close.
vs DT880 (250) - SRH940 wins everywhere here EXCEPT comfort. Sonically it is better than the Beyer's in every respect, and it IS comfortable. If I had to rate it time wise, I would say I could wear the SRH940 for 2 hours without starting to feel uncomfortable, but the Beyers I could wear all day. My DT880's will be movies only from now on, as for music, they are currently my 4th choice.
vs TMA-1 - Just about as easy to drive as the TMA-1 which surprised me, but while I feel the TMA-1 sees NO improvement from amping, the SRH940 leaps ahead once you give it some juice. For electronic and Ambient, which I listen to a lot when I travel, I actually think the TMA-1 will still be a go to. The TMA-1 leaks just a little bit less, although both are VERY loud, before they would entrude on anyone around you. I would probably sell my TMA-1 if they did not look so cool.
My 2 cents anyway.