Open-cell or closed-cell spray foam: which one should I use?

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The two products are used for different jobs, and a quote specifying one is not automatically better or worse than a quote specifying the other. What matters is whether the choice matches the assembly. Closed-cell is dense, roughly 2 pounds per cubic foot, at about R-6 to R-7 per inch. It is a vapor retarder at typical thicknesses, it adds racking strength to a wall, and it does not hold water. That combination makes it the standard specification anywhere moisture is in play or space is tight: rim and band joists, crawl space walls, the underside of a roof deck in an unvented assembly, and any below-grade application. Open-cell is light, roughly half a pound per cubic foot, at about R-3.5 to R-4 per inch. It is vapor permeable, which is sometimes the point, because it lets an assembly dry in a direction closed-cell would block. It expands far more, so it fills irregular cavities well, and it is a better sound absorber. Cost per board foot is meaningfully lower. The practical decision rules. In a 2x4 wall where you need every point of R-value from 3.5 inches, closed-cell. In a deep attic or a 2x6 cavity where inches are available, open-cell often delivers the same total R for less money. Where the assembly has to dry inward, open-cell. Where you are stopping vapor as well as air, closed-cell. Against fiberglass and cellulose: batts have no air-sealing function and their rated R-value assumes perfect installation, which is rare. Dense-pack cellulose air seals reasonably well and costs less than foam, and it is a genuine alternative in closed wall cavities. In Climate Zone 5A the attic target is R-49 to R-60 depending on the adopted code cycle, and blown cellulose or fiberglass over a properly air-sealed plane reaches it at lower cost than foam. A good contractor should be able to say why they specified what they specified for your assembly.