Could go either way. Based solely on Asmodel's battle with Superman Blue, I believe Monarch certainly has enough power to prevail. However, if Asmodel utilized 'the light of Heaven' against Monarch, he would likely win- as I doubt that Monarch has a pure enough soul for the light to be rendered ineffective (as it was vs. Superman.)
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."
It should be noted, at the very least, that Superman Blue did not defeat Asmodel. He was defeated when Wally and Kyle created the vibrational frequency needed to BFR the Angels. There's no reason for Monarch to know to do that, assuming he's able to.
I don't really know what "true form" Asmodel would be, but going by hype and the power of other top-tier angels, he should be able to pull out the win here. Maybe. Probably...
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"And then there was nothing. A once broken something now void.
And on the first day, Doom spoke... 'Be.'
And then there was life."