Comparing the two fragrances…

Dior

Gritti
Miss Eau Fraîche
Damascus
Only in Miss Eau Fraîche
Only in Damascus
Shared character
Both Miss Eau Fraîche and Damascus share citrus accords and the inclusion of Indonesian Patchouli.
How they differ
Miss Eau Fraîche is characterized by floral, chypre, green, and fresh accords, featuring notes of gardenia, bergamot, and Calabrian bergamot. In contrast, Damascus focuses on woody, tobacco, spicy, sweet, resinous, amber, balsamic, and warm spicy accords. The note profile of Damascus includes orange blossom, sandalwood, elemi, neroli, amber, cinnamon, myrrh, orange, tobacco, Sicilian orange, and Ethiopian myrrh.
Who each suits
Miss Eau Fraîche suits those who prefer fresh, green, and floral profiles. Damascus suits those who prefer warm, spicy, woody, and resinous profiles.