A few possibilities.
If you're listening to music that's dynamically overcompressed, which a lot of modern music is, then yes when you crank it on a high-rez headphone it will sound like a distorted mess. That's because "distorted mess" is exactly what it is.
Your source could be not up to par, as others have said, though somehow I doubt it.
Your files could be really poorly encoded, and a more revealing headphone will sound worse than a cheap one since it shows you that something's wrong.
It could simply be broken. A working MS-1 should not be getting bested by random $20 cans.
Or, you could simply be hearing the inherent distortion present in all dynamic drivers. If you're listening to really fast and dense stuff, like death metal or very complex electronica, then most dynamics simply can't keep up. Here you will need electrostats, or orthodynamics at the very least. I also think that with most dynamics stuff like Nile turns into a distorted mess. But before you commit to a 'stat system (which doesn't have to be very expensive, check out the Stax SR-001, SR-005a, and 2050 systems, or a Koss ESP950), you should rule out all of the possibilities above.