These are not competing qualities so much as different tools. Here is how the decision actually gets made.

Choose etch for permanence

Etching removes material, so there is no coating to fade, abrade or peel.

It survives every dishwasher, forever, which is why awards and hotel stock use it.

Choose print for colour

Etch renders as one frosted tone. Gradients and photographs do not translate.

Fired ceramic print gives colour that also survives commercial washing.

Mind the stock when etching

Tempered glass holds its strength in a thin compressive surface layer.

Deep cuts into that layer risk the piece, so shallow frost is the rule on barware.

Combining the two

An etched mark on one face and a small fired print on the other reads beautifully.

Just decide it deliberately, and proof the set assembled rather than piece by piece.