I got a pair of DT150 over the SRH940. The real strange thing about the Shure is that after burning-in its sound signature just tend to disappear. I have experienced with my old SRH840 and with 940s one burnt-in demo pair and a brand new one. The demo pair sounds noticeable less bright and speedy sounding, the bass stayed around the same. I liked their brand new sound signature, but burnt in it is pretty unspectacular sounding imo. Also with their silver plastic finishing + swivel earcups, it is less well built than the 840, even the comfort is greatly improved. With silver, the horrible plastics mold seams are very visible and is a total eyesore, it also makes me wonder if the silver paint is going to come off in time or not.
For me, the DT150 have around the same detail and great treble like the SRH940 but have great bass and neutral mids. I found their bass one of the best I have hear from a closed back dynamics, and its build... a tank made in Germany. Compared to the poorly built Shure made in China it is hard for me to choose the Shure over the Beyer.
The SRH940 is still more easily to pick up more micro details than the Beyer for sure and doesn't need an amp to drive too, where the DT150 is a must.