Sheathing the outside of your home with continuous rigid insulation is like blanketing your home: it provides a continuous insulating barrier that acts as a thermal break (reduces heat conduction through the wall). Normal cavity insulation still does the heavy lifting on most homes in terms of reducing heat transfer through the wall, but most residential walls also have studs in them, which interrupt the thermal resistance of the insulation. Wood is not a good conductor, but it is a conductor, and since it passes through the width of the wall, we need something over the wood that is less conductive if we want to break the conductivity. This is where rigid insulation comes in.
Code in our area requires a wall with a minimum R-value of 18 (its actually more complicated than this, you can technically get away with less, but this is the recommended minimum). That amounts to a 2x4 wall blown with dense-packed fiberglass, and 1/2” of rigid insulation on the outside. R-15 for the cavity, and R-3 for the rigid sheathing.
However, those R-values assume that there is no thermal bridging in the wall, like the wood studs. It is estimated that the typical thermal bridging in a residence can reduce the nominal r-value by as much as 20%.
On our standard building envelope, we specify 1/2” rigid insulation around the exterior of the conditioned space. Over a 2x6 wall with dense-fill fiberglass, yielding an r-value of R-25. Combined with our high performance air sealing package, you get a wall that keeps air in and heat out more effectively than the code-minimum built wall. This is a cost-optimized solution that acts both as the water-barrier and the structural sheathing (when paired with structural foam sheathing and the proper sealing methods), saving on labor and additional material to install separate products for these functions. This system has been field-tested for the past 30 years, with solid empirical results.
Rigid insulation does add to the cost of the home, but the added cost is minimal compared to the payback via lower energy bills, I would guestimate its less than 5 years. Add to that the increased comfort, reduced loads on the HVAC system, and we think its a must-have for our climate.