There is a command called ctrl_mode, which you can set to 0x01 for DMC and 0x02 for CTRL (Hint: don't forget to set also CTRL ctrl to activate the control for CTRL!).
Years ago, when I was a student and used a hummingbird for my research, there was only DMC available and nothing else. It is only an old standard, which we use for easy output maping (0-100% or -100 - +100%). Of course, you have a higher output range with CTRL commands, so I prefer to use that.
DMC is reported to control pitch, roll or yaw RATE, while CTR controls pitch, roll angle directly, or yaw rate.
What CTRL does is quite clear: it is simply a reference to the internal attitude controller that runs on the LL processor.
But what does DMC do? To the best of my understanding (even if I did not found any references or documentation to this) it controls the differential velocity between the propellers, which therefore generates a torque (proportional in some sense to the square of the prop rotational speed), which actuates the attitude dynamic.
If it is like this, DMC does not control the angular rate (first derivative of angles) but the double derivative of the angles (angular rate rate).
Or does DMC really controls the angular rate? With a lower level control law on this dynamic?