What are the advantages and disadvantages of each method?
I suspect that mist is more expensive, but covers a larger area of the tree roots.
Mist is used in some nurseries and not for fruit trees. Overhead sprinklers or drips are used to trees. Both have pros and cons. Overhead wets leaves and expose them to diseases. It wastes water too. But if you have whiteflies issue, overhead can help reduce their population. Drip saves water but it is more expensive to setup, but running cost is low.