Different ears, different preferences - you can't change what you like and don't like. I'm very much into natural/balanced sound (even though the two don't go together sometimes). I personally found the SRH840 sounded a lot more natural than the SRH940 (940 to me very warm - but sweet and dry rather than dark - very coloured).
I could absolutely enjoy the 940 with female vocals, folk, jazz, and some classical. Didn't do it for me with rock. And eventually I want one good open can (HD600), a contrasting fun can (so far the MS1i), but I'd like one neutral closed can that will do any genre. I may yet go back to the SRH840 - but I want to try the FA-003 first.
And to answer your above question - you're missing nothing - congrats on the SRH940 ..... enjoy them!
My goal as well.. And I also did find the SRH840 more natural than the SRH940 but it loses clarity and "sharpness" in the process. I will!