Which decoration method the agency should be choosing
The studio is the only party that can weigh a brand requirement against a production constraint, because the studio knows what the mark has to do and the supplier knows what the process will do to it. In practice that means the studio decides the intent and the supplier advises on feasibility, and the decision should be written down as a sentence in the brief rather than left to emerge from a sample.
Flat spot colour, one to four colours, larger runs. This is screen printing, and it is the default for a mark on a garment body at volume. The artwork stays exactly as drawn, the colours are mixed to a named reference and can be checked against it, and the per-unit cost falls as the run grows because the setup is recovered. The constraint is that every additional colour is another screen, so a design that gains colour at review time is gaining money at the same time.
Photographic, gradient or continuous-tone artwork. This is digital direct-to-garment, and no volume makes a halftone approximation of a photograph better than a digital print of the same photograph. The studio should expect the result to look like the layout rather than like a screen rendition of it, which is usually the point. The trade is that a digital press is a process-colour device, so a named spot colour in the brand book cannot be hit exactly, and where the brand colour is contractual the mark and the image should be split between two methods.
Small runs, or a design that will be reordered in variants. Below roughly a hundred units, setup dominates the unit cost, and the method with the smaller fixed cost wins regardless of the artwork. This is also the case where a design exists in several colour variants or several garment types, because each new colourway on a screen-printed garment is a new set of screens rather than a new press run.
Premium perception, or a mark that has to survive hard washing. Embroidery carries a visual weight that printing does not and survives far more wash cycles, at a higher unit cost and with real constraints on detail. Embroidered marks must be simplified: fine gradations do not exist, small text disappears, and the minimum element size is governed by the stitch, not by the screen. The studio’s job is to redraw the mark for the process rather than to send the print version and let it fail.
Technical fabrics, dark garments and full-bleed graphics each have their own answer, and in every case the answer is decided by the substrate and the artwork together rather than by preference. The productive question to ask the supplier is not which method looks best but which method can hold this specific file at this specific quantity, and the answer changes when either of those two things changes.