Given the forthcoming launch of the James Webb Space Telescope (JWST), which will allow observing exoplanet atmospheres with unprecedented signal-to-noise ratio, spectral coverage, and spatial resolution, the uncertainties in the atmosphere modeling used to interpret the data need to be assessed. As the first step, we compare three independent 1D radiative-convective models: ATMO, Exo-REM, and petitCODE. We identify differences in physical and chemical processes that are taken into account thanks to a benchmark protocol we have developed. We study the impact of these differences on the analysis of observable spectra. We show the importance of selecting carefully relevant molecular linelists to compute the atmospheric opacity. Indeed, differences between spectra calculated with Hitran and ExoMol exceed the expected uncertainties of future JWST observations. We also show the limits of the precision of the models due to uncertainties on alkali and molecule lineshape, which induce spectral effects that are also larger than the expected JWST uncertainties. We compare two chemical models, Exo-REM and Venot Chemical Code, which do not lead to significant differences in the emission or transmission spectra. We discuss the observational consequences of using equilibrium or out-of-equilibrium chemistry and the major impact of phosphine, detectable with the JWST. Each of the models has benefited from the benchmarking activity and has been updated. The protocol developed in this paper and the online results can constitute a test case for other models.