I have used the Bose X for 3 years and while I have not flown with the D-C I did test this during a fairly careful comparison of various headsets I did in both a headset shop equipped with an aircraft noise source and in an actual plane on the ground.
My view is that the Bose is better overall. The total attenuation of both is the same. The D-C has more passive attenuation but a lot higher earcup pressure. The Bose appeared to reproduce speech more clearly.
While this applies to all headsets, with the Bose you especially need to avoid using glasses which are too thick at the point where they pass under the earcup.
I think the Bose is less sturdy than the D-C so it's OK if you use it yourself only and look after it. In particular, if you get the aircraft-powered version, the connectors are flimsy and break easily.
I think the Bose is far more comfortable although this may not be apparent on short trips.