This is one of the most misunderstood questions in the trade. A mesh does not make a screed unbreakable, nor does it prevent cracks from appearing. Its role is more modest and specific: to keep the edges of a crack tight so that it remains invisible and inconsequential beneath the flooring.
Conversely, on a bonded screed that is thin and directly attached to the slab, mesh provides almost no benefit: the slab is already doing the work.
Fibers, whether polypropylene or metallic, are mixed directly into the mortar. They distribute resistance throughout the entire mass and effectively manage shrinkage during the initial setting phase. Mesh, on the other hand, acts in a single plane but is better at handling bending stresses on deformable substrates.
The two are not mutually exclusive: for a large-area heated screed, combining fibers and mesh is common. On an anhydrite screed, however, shrinkage is so minimal that reinforcement is generally not required.
Mesh laid flat on the insulation and then covered with mortar is useless. It must be positioned within the mass, approximately in the lower third or at mid-thickness, which requires lifting it as you go or placing it on spacers. The panels should overlap by at least one mesh width, and the mesh must never touch the perimeter strip, otherwise you risk creating the rigid bridge you were trying to avoid. If placed incorrectly, it won't hold anything the day the screed cracks.