There are any number of Justice League members who are a match for Dr. Manhattan in “reality-altering,” including, but not limited to: Zatanna, Dr. Fate, the Spectre, and the various Green Lanterns (plus Guy with Sinestro’s ring). Since Dr. Manhattan is really a stand-in for Captain Atom anyway (all the Watchmen are analogues of the Charlton Comics characters DC acquired: Rorschach = Question, Owlman = Blue Beetle, etc.), we know Captain Atom is a match for him (Captain Atom being JLE, so he qualifies). Firestorm could probably handle Dr. Manhattan from a quantum standpoint (and would squish Dr. Manhattan like a bug after becoming an elemental). There’s just no way the Watchmen stand a chance. It’s not the same power scale.
I’d bet on an eternal tie. Earth loses by getting destroyed in the process along with half of the solar system.