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I'm not really sure if this is a good match or not, honestly. I just think that they have some similarities based on their psychology and attitude towards the universe.

Ego wants to assimilate the universe, and he has shards of himself planted on every planet in the solar system. Doctor Manhattan has just gained a new appreciation for life, and does not want this to happen.

R1: Doctor Manhattan is on Earth. Can he traverse the universe to make it to Ego's planet in time and destroy his brain without getting destroyed by Ego?

R2: Doctor Manhattan is on Ego's planet. Same scenario. Is there anything that Ego can actually do to hurt Jon?

Sorry for the massive spoiler text block, but this is spoiler territory for GotG Vol. 2:

While Ego was one of the best MCU villains to date, his power to build up his planet and go throughout the cosmos to plant shreds of himself everywhere was the long game taken to the longest extent.

Yondu, Rocket, Gamora, etc. were holding Ego's tentacles at bay for a bit before he overwhelmed them and then Peter came to the rescue to the tune of Fleetwood Mac's "The Chain". That tells me Manhattan for sure can win Round 2, as Osterman should be able to disintegrate/matter manipulate enough of Ego until he gets to his brain and disintegrates it. Round 1 should be the same if the Doc knows where Ego's planet is, as he nigh-instantly teleported to Mars. It seemed that wherever he wanted to port to, he did it in however long it took him to think it.