X-ray phase contrast imaging (PCI) denotes a group of highly sensitive imaging techniques that permits imaging at scales ranging from nanoscopic to the medical. Recently introduced, speckle-based imaging has seen a rapid development because of its experimental simplicity and its capability to retrieve the refraction, the scattering and the absorption of a sample using a conventional X-ray set-up. Precise simulation would permit to optimise the imaging setups for different applications, but until now works on simulation of X-ray speckle-based phase contrast imaging have been very few. In this work we evaluate different simulation codes, based on Monte-Carlo, analytical ray-tracing and wave-optics Fresnel propagation. The simulation results are compared to both synchrotron and conventional imaging experiments to permits their validation. We obtain a strong similarity between simulated and experimental data. We discuss the validity and applicability of each approach.