They are different, to be sure, but I'm probably one of the few that would understand your reasoning. Having both the M50 and MD, may I suggest listening to some streaming radio stations, preferably something that offers higher quality files, such as MOG music, Spotify, or Google Play all access. Most offer a trial period, at least in the US.
The reason I suggest this is because most of my music that I was listening to prior to getting the Mad Dogs was discovered with the M50 or Denon D5000. The songs I enjoyed the most sounded great with these headphones, which tend to have a V-shaped sound signature when compared to the Mad Dogs. I have since "rediscovered" some old favorites and found a bunch of new music that sounds very sweet with the Mad Dogs, where this music loses a bit when listened to on my other headphones. And while you may not notice much of a difference with the songs you've been listening to with the M50, you might be surprised about how different some other music sounds between the Mad Dog and M50.
If you aren't already doing so, explore some new music, or go back and try some old songs that may have lost their spunk. The Mad Dogs have taken some music that was previously only ok to me and made it sound very special. For me, the Mad Dogs shine with Jazz and Latin genres. I've also found that I really enjoy classical guitar and various folk music significantly more with the Mad Dogs.
With regards to the differences between the Mad Dogs and M50, I feel that I am not losing much with some songs, but I'm gaining so much more with others. If that makes any sense.