We have an unheated crawlspace under our house that we would like to insulate.
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We live in Florida (about 50 miles southwest of Jacksonville). We have a 2.5 to 3-foot crawlspace on our house and we have two access points on the east/west side of the house. There is some old insulation in floor joists held in place with older fiber-type board (black in color). We want to remove this and reinsulate with 3-4" polyiso insulation boards. Would we want to use foil-sided board or unfoiled board?
It's not quite clear from your question whether you plan to remove both the existing between-joist insulation and the fiberboard and put the new boards between the joists or if you are planning to install them over the joists for a faster insulation.
I suspect you are planning to remove it all and put new insulation between the joists. Note at this point that it may be more cost-effective and especially labor-effective to use spray foam while getting a superior result (directly attached to subfloor without any gap, perfect seal to the joists).
Now to your question of foil-sided or not. I really see only very limited benefits of the foil in your climate in a crawlspace location, considering you are using 3-4" polyiso boards so you are getting an R-value of 21-28. At that point, the temperature difference between the inside face of the insulation and your house should be minimal.
Contact me directly if you want to discuss this further, and look seriously into home foam insulation instead.