In general Cayman will have better selection on black coral [they grow it there] and Ammolite.
Cozumel will have better selection on most semi-precious stones [opals, topazes, amethysts, peridots, sapphires].
It's six-one, half dozen-other on diamonds, emeralds, alexandrites and tanzanites.
If you need a custom-made anything while in port on a Western cruise, go to Cozumel: Rachat y Romero. One of the cruise "recommendeds".
If you're Eastern Caribbean and you need a custom-made while in port, the only place that can do it is Gem Casa in the Royal Dane Mall on St Tom. Not one of the cruise "recommendeds", but all the "recommendeds" know them and recommend them.
Desperately seeking 10th cruise for the free laundry.