the MM can grant it's 'wisher' absolutely anything he/she can possibly imagine. it is, for all intents and purposes, the ultimate 'power' in the DCU. however, it has always been portrayed as a 'one trick pony', so to speak [ie. one 'wish' per showing is all that's really been depicted concerning the MM] - though a single 'wish' is all that's ever needed in the end, meh... whereas a CC can also grant it's user damn near anything, yet that 'trait' [or whatever] has been used back, to back, to back.
so in terms of versatility [if that's what it'd still be called] i'd say a CC might have the edge. but in terms of overall power output, i'd go with the MM.
i dunno, it's hard to call 'battles' like this, where opinion plays the biggest part. *shrugs*
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."
Most of its showings in the Legion, Final Crisis, etc. In the latter, it basically erased Darkseid, who had merged with all of reality, and reset the DC multiverse to make Superman's "happy ending."