Fluidization of soft glassy materials (SGMs) in microfluidic channels is affected by the wall roughness in the form of microtexturing. When SGMs flow across microgrooves, their constituents are likely trapped within the grooves' gap, and the way they are released locally modifies the fluidization close to the walls. By leveraging a suitable combination of experiments and numerical simulations on concentrated emulsions (a model SGM), we quantitatively report the existence of two physically different scenarios. When the gap is large compared to the droplets in the emulsion, the droplets hit the solid obstacles and easily escape scrambling with their neighbors. Conversely, as the gap spacing is reduced, droplets get trapped inside, creating a "soft roughness" layer, i.e. a complementary series of deformable posts from which overlying droplets are in turn released. In both cases, the induced fluidization scales with the grooves' density, although with a reduced prefactor for narrow gaps, accounting for the softness of the roughness. Both scenarios are also well distinguished via the statistics of the droplets displacement field close to the walls, with large deviations induced by the surface roughness, depending on its stiffness.