Originally posted by Inhuman
All of that was pretty much covered in Watchmen
So? DC would be making a mistake by not examining this subject when it applies to one of their characters so well just because "Watchmen pretty much covered it". It would break the "realistic" setting that they set the universe in to ignore it.
Also there are some significant differences between Manhattan and Kal-El. Kal comes from the stars and lived among us in secret for decades until violent members of his own race forced him to come out of hiding. His motives, as I doubt he gives interviews, are unclear and thus take any and all forms born from the public's imagination ranging from savior to dictator.
Manhattan on the other hand is known to be an ordinary man who became a god-like being. This grounds and rationalizes his existence/potential purpose. It is also known that he is an ally of the American government. Thus, it is reasonable to assume he is treated with nervous acceptance at worst in America as the people believe the government has him in check, and feared abroad as America's greatest weapon.
TL;DR: The public narrative on Manhattan is more or less written by the beginning of Watchmen where as it is just beginning to be forged for the Man of Steel. This difference is what not only makes the subject worth examining in BvS, but gives us the opportunity to possibly go deeper than the Watchmen film did on the matter.