2H, 4H, 6H represents the hexagonal polytypes, and 3C for cubic. My query is which one is best for refractory grade and how it differs from other grades. 15R is for rhombohedral & perhaps not good enough compared to other grades.
You should look for the properties like excellent thermal and chemical resistance, refractoriness under load, thermal spalling behaviour, nature of refractory like acidic, alkaline or neutral depending upon the requirement of the material concerned. Check these properties before you identify the right material.