Clearly there are two halves in a struggle with WCV's who fight their Hunger, psychologically. With RCV's, I'd call it a physical need to feed and RCI have their bodies altered to desire blood, in order to complete the mystical transformation into a monster.
Perhaps the imagery we have of WCV's and their Hunger, as a personified/antropomorphic demonic entity 'living in their heads' is wrong, but it is what we have, plus: Thomas clearly fights his Hunger and gets mental consequences because of it. Following through on that logic, any magical tattoos would probably have mind magic woven into them. Beyond what that might mean for the one who creates them, consider what such magic would do to the vamp's mind: it might calm the Hunger, but at the cost of them becoming psychopathic sociopaths?
So, simply put: in my mind the difference between RCV and RCI, when compared to WCV is body vs mind (apart from the supernatural aspects, of course). Reds' needs are physical and the tattoos the Infected get, inhibit those physical reactions. Whites' needs are psychological, so logically, their tattoos would need to affect their minds. And we all know how good mind magic is for our sanity, now don't we kids? :p