from state.gov, all rights to them.

Duties of the SecState
(My view between Petraeus, Romney and Giuliani)

Serves as the President's principal adviser on U.S. foreign policy; (Petraeus based on his military & CIA background)
Conducts negotiations relating to U.S. foreign affairs; (Petraeus and Romney tied, Giuliani maybe be a little hot headed)
Grants and issues passports to American citizens and exequaturs to foreign consuls in the United States; (All three can appoint people to do this)
Advises the President on the appointment of U.S. ambassadors, ministers, consuls, and other diplomatic representatives; (Petraeus knows more than Romney on this)
Advises the President regarding the acceptance, recall, and dismissal of the representatives of foreign governments; (All three can do this, as they would all be advised on this)
Personally participates in or directs U.S. representatives to international conferences, organizations, and agencies; (All three can do this, I could do this))
Negotiates, interprets, and terminates treaties and agreements; (All three can do this with Trump's direction, nothing doesn't go through Trump))
Ensures the protection of the U.S. Government to American citizens, property, and interests in foreign countries; (I lean toward Giuliani on this one for his law skills over Petraeus for his military skills)
Supervises the administration of U.S. immigration laws abroad; (Giuliani wins here as this is what he is focused on)
Provides information to American citizens regarding the political, economic, social, cultural, and humanitarian conditions in foreign countries; (Romney on this one, as he is more social based on things like healthcare)
Informs the Congress and American citizens on the conduct of U.S. foreign relations; (All three can do this)
Promotes beneficial economic intercourse between the United States and other countries; (Romney is more a businessman)
Administers the Department of State; (All three can direct others to run the day by day)
Supervises the Foreign Service of the United States. (I was going to say Giuliani but am going to be fair and say all three can do this)

So, with all that said. On being able to do the job and experience, each get 2 votes, with the rest being ties.

Now it comes down to integrity (the state of being whole and undivided): Giuliani wins as he has been whole and undivided towards Trump. If Giuliani was out of the picture, then Petraeus over Romney just because of the Romney rant.

So, I would give it to Giuliani.
Petraeus second
and Romney last

or Romney if you want pretty.

But its all down to what Trump wants, media is leaning Romney at this moment.