At distances from the active galaxy nucleus where the ambient temperature falls below ̃1500-1800 K, dust is able to survive. It is thus possible to have a large dusty structure present that surrounds the active galaxy nucleus. This is the first of two papers aiming at comparing six dusty torus models with available spectral energy distributions, namely, Fritz et al., Nenkova et al., Hönig & Kishimoto, Siebenmorgen et al., Stalevski et al., and Hönig & Kishimoto. In this first paper we use synthetic spectra to explore the discrimination between these models and under which circumstances they allow us to restrict the torus parameters, while our second paper analyzes the best model to describe the mid-infrared spectroscopic data. We have produced synthetic spectra from current instruments GTC/CanariCam and Spitzer/IRS and future James Webb Space Telescope (JWST)/MIRI and JWST/NIRSpec instruments. We find that for a reasonable brightness (F 12 μm > 100 mJy) we can actually distinguish among models except for the two pairs of parent models. We show that these models can be distinguished based on the continuum slopes and the strength of the silicate features. Moreover, their parameters can be constrained within 15% of error, irrespective of the instrument used, for all the models except Hönig & Kishimoto. However, the parameter estimates are ruined when more than 50% of circumnuclear contributors are included. Therefore, future high spatial resolution spectra such as those expected from JWST will provide enough coverage and spatial resolution to tackle this topic.