Open-cell is also known as half-pound foam. It has an R-Value of 3.5-3.6 per inch, and its density is bout 0.5 pounds per cubic food. Low-density foams like these are made partially from raw biological materials Carbon dioxide or water is also used in the makeup. Open-cell uses far less material than closed-cell, but its R-Value is lower. Also, open cell requires a vapor retarder (like gypsum wallboard) and is riskier when used for roof sheathing. It's not highly recommended that you use open-cell insulation if you live in a cold climate unless you have that extra barrier. You should also compare how much money you spend versus how effective the open-cell insulation is wherever it's installed.
Closed-cell (aka two-pound foam) is denser than open-cell at about 2 pounds per cubic foot. Its R-Value is between 6-6.5 per inch. As a result, this kind of foam is much more expensive than its counterpart. The reason closed-cell doesn't need a vapor retarder is because it already has one. It's permeance is 0.8 perm, which means it can handle cold climates without the use of an additional board or drywall. Closed-cell uses hydroflurocarbons (HFCs) as part of its makeup. However, this material has been known to have a high global warming effect. If you want a green insulation solution, this is not the material to use. A way to avoid this and still use closed-cell is by installing it alongside fiberglass batts.
If your foam pulled away just a little bit, Jamie, and they were able to fix it with just a little bit of touching up, then it wasn't as bad as the house where I saw this problem. As the last photo above shows, it had pulled away significantly from the studs and rafters, and it was all over the house. This was closed cell foam, and interestingly, it didn't pull away from the horizontal framing members, just the vertical and sloped ones. They did some touch up, but that wasn't enough. I don't know how this one ended up getting resolved. I think maybe the contractor came back and sprayed cellulose on top of the foam.