DoS Doomsday and DoS Superman vs the Asgardian Destroyer...
Superman and Doomsday as they were during the Death of Superman storyline vs the Asgardian Destroyer in a battle to the Death or KO with no BFR allowed...
Going by their appearance in DOS, The Destroyer stomps. But with all the stuff retconned in, would be a decent fight with the Destroyer eventually being triumphant. The Destroyer actually needs to put Supes down first and DD second and specifically in that order because otherwise Superman could occupy the Destroyer long enough for DD to heal and evolve and then it would be a stalemate between those two with a dead supes.
By the time of DoS, Doomsday had already taken and survived a blast from a Guardian of Oa suicide-exploding. Something which tore a hole in space itself:
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I reckon that's far beyond what we've seen the Destroyer do, when animated by Loki.
The longer the fight goes on, the more Loki will be subjugated. He's strong, sure, but he has limits.
Not that I know of. Of course, as per the OP, I am stopping at DoS Doomsday (i.e. any showings after this are null and void).
He faced the Radiant, who took a week of fighting to bring him down (which, honestly, I can't see Loki lasting THAT long in the armour). The end explosion took out 20% of the planet (I don't know how big that planet was).
And even this did nothing but KO him.
So by the time DoS rolls around, the version of Doomsday we see is evolved PAST energy attacks. As shown when MM/Superman/Booster/Guy/Fire all simultaneously bust all over him at once and he just laughs it off.
I see what your saying. Very possible. Not entirely sure how much it will actually drain Loki as he operates it from another place and he is not physically in there. If Loki can use his own magic while in the Destroyer he can dominate through tp and trickery. These are about the two toughest people I could imagine on putting a physical beatdown on.
What would happen if Supes vibrated his hand through the Destroyer skull? Nothing or would it burn him?
Destroyer will beat them down period, Destroyers has unlimited strength, Stamina, very high invulnerability energy manipulate plus the wearer powers also, which mean if Loki is physical wearing the armor it's the armor powers plus his own. If he is mentally inhabiting the armor then it's just the armor powers which is at trans level if the person know hows to use the armor properly.