I have both and would like to add it with roasted figs, but which one?
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I would use the green. The green pods are what the world really knows as cardamon and typically the only ones used in baking. Both are used in savory dishes but black is much less common and used more for stronger applications...spice rubs. spice mixes, meat stews etc. You should only buy it by the pod as the essential oil disappears quickly once the pod is opened and even more quickly when ground.
Do the pods need to be grated or broken to get the flavor to permeate in sugar syrup?
If the pod is fresh(green and not too shriveled and can smell the cardamon without opening the pod) just opening the pod and allowing it to sit among the roasting figs should be fine. You can always grind a seed or two if you want according to how much flavor you want.
I have used black cardamon (just a tiny bit) to enhance chocolate sauce for a spicy flavor. It can be used for dessert applications, although very sparingly.
I use black cardamon pods for broth. I just throw a whole pod in the pot. I bought them in Vietnam and the flavor is very intense and, yes, kind of smoky. I believe that they are just another variety of cardamon, however. I have only ever seen green cardamon at American stores.