Generally speaking it's a win for Doomsday, but can he do anything that would reduce Nimrod to individual molecules, which is what's required for a true win in this battle? Nimrod can still self-repair at the molecular level, so it's awfully hard to actually destroy him.
Nimrod could easily BFR him by reversing his gravity, and could easily avoid him by teleportation, but I don't think he could ever beat him in combat. He does have a pure disintegration beam that does completely reduce its target to atoms. I don't know if Doomsday has ever shown resistance to something like that, although I assume so. Could Doomsday resist tele-dismemberment?
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