Baking powder is a leavening agent. Baking soda is not by itself, but add cream of tartar and it is -- or if you use a sour product (buttermilk or soured milk).
As for making the cookie softer -- that depends on the recipe and ingredients you have to work with. Several ideas already listed work (extra egg for drop cookies), but it's also good to check the recipe to know if you should sift the flour or not. It may not be a choice of BP vs. BS Hey, if the cookie is too hard, have a cuppa coffee or glass of milk with it. It's the taste that counts!