Really a matter of taste, if it's not specified; Dark will have a little bit more moisture, but nothing significant. Personally, I'd go for dark.
Not an answer, but ooh apple cake, could you please share the recipe?
Dark brown sugar is going to have a higher molasses content than light, and therefore a slightly higher acid content. If using dark, perhaps bump the baking soda by 1/8 teaspoon.
Typically, if a recipe doesn’t mention which, it means light. But as other have posted it is a matter of taste.