I'm going to try and keep this short and simple.
I had james mcprogger ask me to compare these a month ago.
The shure srh 940
These are meh, the vocals sound atrocious. Every thing else sounds great however. They are great for rock and metal due to the mids and highs emphases. They are bad for electronic.
They are not bassy and to many lack bass. Vocals are very fake sounding. They sound muffled to me. This are smooth and non fatiguing. These are hard to drive and perform poorly from a portable source like an iphone.
Sennheiser hd 25 1 ii
These are imo the best portables under $200. The bass is emphasized enough to give it a good thump for electronic. The highs are well extended and the mids are well presented. These are v shaped frequency curve headphones. They can be however harsh on many recordings and source matters. These are relatively easy to drive and any portable player should handle it fine.
For rock and metal music
For you metal heads out there the sennheiser hd 25 1 ii is vastly superior. Much funner and more realistic sounding.
For electronic and bass music
Again the sennheiser hd 25 1 ii is much superior but thats to be expected.
For acoustic, folk, classical, and jazz
Here is where the shure srh940 does well. But be warned if there is any vocals in the track it will sound awkward.
The hd 25 1 ii is a much superior headphone in every aspect except sound stage.
Avoid the shure srh940 like the plague. It's shures version of the beats. About 2x over priced for what it is.