Various sizes of rope and grades test different aspects of cutting ability and thus all have merit. For example, the cutting ability of a knife depends on its sharpness, the edge angle and width, and the primary grind angle and width (in that order). As the rope gets smaller you see less an influence of the latter listed aspects and you tend to concentrate on the first. At the extreme end, cutting thread is almost a test of pure sharpness.
In regards to type, the harder ropes (synthetics mainly) are much more difficult to cut, and are generally more abrasive. A knife that can push cut hemp very well, and even slice it decently, may not be able to cut poly ropes at all because the edge isn't aggressive enough. So I would suggest that you experiment with different ropes, as they all tell you something, figure out what this is, and then choose some that are complementary and go with them as standard reference materials. For example 3/8" hemp and 1" poly will cover a rather wide range of cutting ability aspects.
-Cliff