Manhattan has a mind, and despite his impressive power set, it is a weakness. Regular humans were able to pressure him into abandoning his life on Earth. Imagine what a telepath would do to him. And that telepath is the Phoenix. The Dark Phoenix. I also think her TK surpasses Manhattan's powers on every level.
DP has access to all of his powers as well but on a much much higher scale. he creates life she creates universes and realities, her telepathy can make a star go supernova, she could create a force field to stop the explosion of a star easily, she also can control sub atomic particles. She would easily beat him shes way out of his league Dark Phoenix has stood down Galactus before.
DM has a very low-level baseline of Say, Molocule Man's power. It is all a matter of scale. But, while MM controls the molecules in the whole Actuality (if he wants to). Doc, has never seen, used, fought of even conceived of power on that scale - DP has.
DP wins by sheer scope.
This kinda shows the whole problem people have with DM in a vs setting against mainstream comics characters, in that for all his implied power and god-likeness, he never had to deal with any of the basic superhero tropes and powers that every other powerful character does.
It's like people say, nearly everything Manhatten did could be achieved by Firestorm or Captain Atom or Silver Surfer and so on, and in terms of power levels in DC/Marvel they're powerful but not that powerful.
So yeah, Manhatten never had to deal with a telekinetic powerful enough to blow up stars or a telepath, so going by their showings DP wins fairly convincingly.
This will probably change soon now DC is pointlessly shoving Watchmen into their continuity. So in a few months when it's probably revealed that DM merged universes and removed a decade of time and casually defeats a bunch of DC characters, then we'll be able to judge him against the characters he's implied to be at the level of far more accurately.
But for now, Dark Phoenix
DM has control over his entire being.
Either DP's tp is tk-based (able to physically manipulate the neurons and synapses of the brain) or it is spirit (soul) based.
If the former, then DM has complete control over his being. He can reform at will. He can even duplicate himself multiple times (each with their own mind), he can become intangible, etc.
If the latter, then there are no spirit or souls in the Watchman universe, no God either.
DM can teleport her head off if he can't just make her explode.