Many ancient societies had theocratic governments. This includes the Hebrews who saw their king as a good shepherd and appointed by God to rule his people. The Babylons who later conquered the Jews were the same way and many Jewish people were put to death for not bending knee to their graven images. The Roman's before making Christianity the state religion could also be considered a theocratic government because Caesar was seen as a god on earth. And when the Christian population began to boom it was natural for the emperor (Constantine) to have a vision from the Christ before battle and there after end the persecution of that people trading in his demigod standing for sainthood which in a way has a lot of the same advantages when it comes to controlling a people. If your a leader appointed by God their is no arguing with you especially if your followers are believers. For them it would be like going against God which is a sin and amongst the once pagan Roman people who were very superstitious this would be a sentence to hades (which is also a pagan concept). This would be a great advantage for an emperor who needed the loyalty of his empire especially an empire that was getting ready to divide itself in two ( which it eventually did any way).
However, the Roman empire had been a pagan society. So, what became of the true pagan believers who refused to convert. For a lot of them it was as simple as adding a new god to the pantheon. But what would become of them when it was discovered they still held in regard other gods besides the Christian god? This partnership of religion and government would be a disadvantage for these people because now they could be condemned not for being criminals but for simply having a difference in opinion.
And as much as it seems that a government united under one religion would experience a lot of unity. Any of that illusion of unity was due in part to tolerant people who kept there mouths shut. This would be an advantage in its own right because government could ran smoothly with no argument but a disadvantage because there is no room for new ideas or differences. All those things required to keep a people moving forward and advancing. Which may be in part the reason why the dark ages were so dark. Not just because of a mini ice age but because for hundreds of years one idea allowing no breathing room for another stunt the growth of civilized society.
All in all the only advantages of a theocratic government would be for the government using that religion to sustain power and for the believers of that religion who would be more then happy to pay taxes to a cause they wholly supported. But it is the differences and the freedom to express those differences that actually keeps a people united and from being stagnate.
That is why our founding fathers separated church and state. Because they learned from the mistakes of these ancient societies.
And why third world countries remain third world countries.