I'm not sure if the color of a lego element makes it any more durable. All modern lego parts are made of translucent ABS pellets and then a dye is added for color. Not sure if the dye alters the mechanical properties or not. Thinking back to technic, there are models that use identical friction pin shapes in different colors. In my experience, none of the recolored pins have had any kind of noticeable difference in strength.
As for the cost to produce a color, I have no idea if it is cheaper to make certain parts in db gray over black or vice versa. LEGO gets its dye from outside suppliers, from what I've heard, but I'm not sure on the specifics.