8ct Diopside (Emerald, 13×10mm, Green) vs 8ct Tourmaline (Emerald, 13×10mm, Violet)

All things being equal, Diopside will face-up smaller than Tourmaline for a given carat weight, because it has higher specific gravity (3.3 vs. 3.06 - this means it's "heavier" compared to Tourmaline of the same size).i Face-up size also depends heavily on the proportions of the cut.

Face-up area is a measure of the size of the gem when viewed from above (as set in a ring). It tells you how big the gem is at the girdle plane.