Assuming we are talking about using a CX designed bike on trails vs. a mtb on trails (that is not CX racing vs. mtb racing).
What I like about CX bike:
-I can ride easily 10-15mi to the trailhead and the ride back often feels great to get that non-trail speed and a steady smooth burn, like a soothing warm down.
-I can be challenged on less technical trails, which are plentiful and often not used by anyone else. I have this personal idea (that is only controversial if I was to impose it on others) that I want the challenge to be more about me getting places on the trail that the equipment, that there is this leap frog race between buidling ever more challenging trails to accomidate ever more advanced bikes (and yes more skilled riders), that I don't want to be part of, but to be clear I am not making judgements on those who do. It is sure fun, I know.

Al