I tend to agree with Spooky and Left Shoe. While it is true that Superman, particularly the Red Son-verse Superman are immensely powerful and immensely dangerous entities (Because calling them a person in this context seems wholly inaccurate) they are both implied to have limits. Unbelievably high and seemingly impossible limits perhaps, but they have them. In my mind, Dr. Manhattan has no limits, and certainly not limits that Superman could easily defeat. Manhattan might lose, temporarily, but he can reconstitute his physical form from scratch, if need be. The confrontation might be epic, and it might be protracted, but if it came down to an open fight I tend to believe that Dr. Manhattan would prevail.
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Of course, this assumes we are at a point in the story where the U.S government could convince Manhattan to fight for them.