Digital micro-mirror devices (DMDs) have recently emerged as practical spatial light modulators (SLMs) for applications in photonics, primarily due to their modulation rates, which exceed by several orders of magnitude those of the already well-established nematic liquid crystal (LC)-based SLMs. This, however, comes at the expense of limited modulation depth and diffraction efficiency. Here we compare the beam-shaping fidelity of both technologies when applied to light control in complex environments, including an aberrated optical system, a highly scattering layer and a multimode optical fibre. We show that, despite their binary amplitude-only modulation, DMDs are capable of higher beam-shaping fidelity compared to LC-SLMs in all considered regimes.