The game rib is usually considered to be a concave, low set (even swamped), and often not patterened for reflection prevention. Raised ribs set higher and usually have a texture on the top surface; they come in a range of widths. The Churchill rib is raised and tapered in the horizontal plane from the breech to the muzzle (supposed to create an optical illusion of longer sighting radius, leading to more precise aiming). Raised ribs can be solid or ventilated. Some ribs have been made adjustable in height and vertical taper.
Mostly, this is about personal choice with a dash of styling and a pinch of utility..