Closed cell or open cell foam for rim joist in Climate zone 5A
I realize closed cell foam would provide a better R value, but which density of foam would the preferred choice to prevent condensation on the rim joist itself in our mixed climate zone?
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An inch of closed cell foam would be sufficient to limit wintertime adsorption into the rim joist from interior moisture drives, fattening out the R with carefully trimmed R15 rock wool batts would be worth it, bringing the R into the low 20s. As long as you limit the fiber-R to R15 max and have a vapor-permeable/semi-permeable interior side air barrier, the risk of condensation at the foam/fiber boundary is also very limited.
If you go more than 2" with closed cell foam the drying rate toward the interior becomes quite low, and requires that the exterior wetting be at least somewhat limited. If there is ventilated/rainscreened siding on the exterior going thicker than 2" would be fine. But it's a VERY expensive at 17-18 cents/R per square foot compared to fiber insulation at 5-8 cents/R-ft^2. As long as you have sufficient foam-R to limit the condensation at the foam/fiber interface, that's the better value.
Open cell foam would be fine if it's 10" thick (R35+) but would otherwise be too vapor permeable to fully protect the susceptible wood.