Some foams are denser than others. A denser foam will provide a higher R factor. I belive the density is measured in weight per cubic foot. Hotsprings uses a 2lb foam.
Closed cell versus open cell. Closed cell foams can trap and retain the heat better than an open celled foamed. Cells refer to the actual "partilcles" of foam. Open celled foam is usally soft and spongelike. Closed cell are denser, harder, and heavier.
You would want a high density closed cell foam for insulation over say, stryofoam.
If considering a full foamed tub, one that has the entire structure (except for the motor compartment fill completely with the foam. This would be from the hot tub skirt (outter wall) to the shell of the tub. No gaps, no areas that have none.
Some lower end tubs use a lighter foam, or do not completely fill the cavity with foam. Tubs like this should be avoided.