The pale-colored disks of palm sugar have a mild taste, and can be used for any recipe which calls for palm sugar, or for that matter light brown sugar. It's that not strongly distinct from granulated sugar in flavor; personally, the only reason I use it is for texture.
The dark brown palm sugar has a distinct caramelized, even somewhat burnt flavor. It adds considerable, distinct, flavor to a dish, even a heavily spiced one. You should use it in dishes which are specifically supposed to have a palm sugar flavor, but should be careful using it in recipes which say things like "Palm sugar or granulated sugar".
It's really like brown sugar vs. molasses. Sometimes you can substitute them, but not always.
There are probably also ethnic differences in which one you want to use for what, but I don't have enough experience of Southeast Asian cuisines to tell you that.