This is the second in a series of papers devoted to exploring a set of six dusty models of active galactic nuclei (AGN) with available spectral energy distributions. These models are the smooth torus by Fritz+ (2006MNRAS.366..767F), the clumpy torus by Nenkova+ (2008ApJ...685..147N and 2008ApJ...685..160N), the clumpy torus by Honig & Kishimoto (2010A&A...523A..27H), the two-phase torus by Siebenmorgen+ (2015A&A...583A.120S), the two-phase torus by Stalevski+ (2012MNRAS.420.2756S and 2016MNRAS.458.2288S), and the wind model by Honig & Kishimoto (2017ApJ...838L..20H). The first paper explores discrimination among models and the parameter restriction using synthetic spectra. Here we perform spectral fitting of a sample of 110 AGN drawn from the Swift/BAT survey with Spitzer/IRS spectroscopic data. The aim is to explore which is the model that describes better the data and the resulting parameters. The clumpy wind-disk model by Honig & Kishimoto provides good fits for ~50% of the sample, and the clumpy torus model by Nenkova+ is good at describing ~30% of the objects. The wind-disk model by Honig & Kishimoto is better for reproducing the mid-infrared spectra of type 1 Seyferts (with 60% of the type 1 Seyferts well reproduced by this model compared to the 10% well represented by the clumpy torus model by Nenkova+), while type 2 Seyferts are equally fitted by both models (roughly 40% of the type 2 Seyferts). Large residuals are found irrespective of the model used, indicating that the AGN dust continuum emission is more complex than predicted by the models or that the parameter space is not well sampled. We found that all the resulting parameters for our AGN sample are roughly constrained to 10%-20% of the parameter space. Contrary to what is generally assumed, the derived outer radius of the torus is smaller (reaching up to a factor of ~5 smaller for 10pc tori) for the smooth torus by Fritz+ and the two-phase torus by Stalevski+ than the one derived from the clumpy torus by Nenkova+ Covering factors and line-of-sight viewing angles strongly depend on the model used. The total dust mass is the most robust derived quantity, giving equivalent results for four of these models.