I've done a few thousand throwing knives with both stamping and etching.
Stamping must be done before heat-treat (with very few exceptions), so you will be grinding over the stamp. This adds complication, requires some forethought, and carries a risk of failure. Etching can be done at any point.
Once you get your stamping process dialed in, the results are very consistent and clean with no surface blemishing. Etching, on the other hand, can be inconsistent with occasional surface discoloration or stains.
The stamp itself is very expensive. This means that logo changes are cost-prohibitive. Etching stencils are comparatively cheap and it is fairly painless to change your art.
The required tonnage of your stamp press is only an estimation until you have your stamp. Because the stamp is expensive and non-returnable, you may find yourself building or buying a press to accommodate your stamp. The cost of the press can far exceed the cost of etching supplies.