I do not know the exact equation but I am currently gathering data on a normal play-through.
I suspect according to my data so far that mission difficulty is strongly affected by the country's current panic level increased by the other countries panic levels on the same continent. I do not yet know if rewards increase the difficulty.
Small differences can be seen in missions under otherwise similar circumstances, for example the first abduction missions had every country at panic 1 and average continent panic at 1. Here I was given the option of an easy mission or a moderate mission, indicating some sort of random variable in the Difficulty calculation.
So far it seems that if an abduction awards a soldier then the mission will be more difficult than a similar mission under the same circumstances but it could also be random.