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Many protocols for wireless sensor networks are proposed in the literature. In most of this work, comparisons are made with existing protocols to show that the proposed protocol provides better overall performance without precise specifications of the simulation environment. In this paper we show that for a given propagation model, the value of its main parameters retained in the simulation process has very significant effects on the quantitative results. To do this, we use an asynchronous MAC protocol that we proposed which was compared with the reference MAC protocol specified in the standard IEEE 802.15.4 in beacon enabled mode. We use a realistic propagation model like log-Shadowing and we modify the parameters of this model. In this contribution, we also vary the capture threshold. We intuitively known that the asynchronous MAC protocol will ensure a better overall performance than the standard, we will try to show the diversity of results by intensive simulations. To the best of our knowledge, there are existing studies that show the impact of different propagation models on simulation results. However, no studies have shown this impact with such an important level of detail. From this study we estimate that when two communication protocols are compared, it is important to associate the performance curves with the precise and detailed conditions used for the simulation and to assess the global influence. According to this influence, a vigilance can be reported on the accuracy of results.