Any type of rigid foam will work from a building science perspective.
Foil faced rigid insulation vs unfaced.
As john clark correctly notes your wall must have a water resistive barrier wrb.
When it s batts or rolls of unfaced insulation it s meant to be used to add r rating values but should be installed behind the faced insulation.
Faced insulation is a little but not a lot more expensive than unfaced simply because of the extra material it includes.
It is important not to mix them nor use the wrong faced insulation product for each task.
Faced insulation products not only use paper they can also use aluminum foil vinyl and even aluminum paper.
The upside is you save money by not having to pay to add your own vapor barrier.
Mostly paper faced insulation is the best choice for neophytes in insulation installations.
What is the right insulation for an attic.
Foil faced foam for exterior insulation and a felt paper weather resistive barrier behind a rain screen.
His method employs zip system sheathing for structure and air sealing 2 in.
Foil faced polyiso is easy to tape.
Unfaced insulation is a type of fiberglass batt insulation which is normally used over existing insulation.
When to use paper faced.
There are many types of insulation that are unfaced such as spray foam and loose fill fiberglass.
Air migrates from warmer spaces toward colder spaces and insulation is designed to help prevent or at least slow that migration.
Choosing the right thickness of exterior foam rigid foam must be thick enough to prevent condensation on the roof sheathing.
From a green building perspective as dana dorsett correctly notes either eps or polyiso is preferable to xps.
Kinds of insulation that don t involve facing of any sort include spray foam blown in insulation and rigid foam boards.