We present near-to-mid-infrared spectral energy distributions (SEDs) for 21 Seyfert galaxies, using subarcsecond resolution imaging data. Our aim is to compare the properties Seyfert 1 (Sy1) and Seyfert 2 (Sy2) tori using clumpy torus models and a Bayesian approach to fit the infrared (IR) nuclear SEDs. These dusty tori have physical sizes smaller than 6 pc radius, as derived from our fits. Active galactic nuclei (AGN) unification schemes account for a variety of observational differences in terms of viewing geometry. However, we find evidence that strong unification may not hold, and that the immediate dusty surroundings of Sy1 and Sy2 nuclei are intrinsically different. The Type 2 tori studied here are broader, have more clumps, and these clumps have lower optical depths than those of Type 1 tori. The larger the covering factor of the torus, the smaller the probability of having direct view of the AGN, and vice-versa. In our sample, Sy2 tori have larger covering factors (CT = 0.95±0.02) and smaller escape probabilities than those of Sy1 (CT = 0.5±0.1). Thus, on the basis of the results presented here, the classification of a Seyfert galaxy may depend more on the intrinsic properties of the torus rather than on its mere inclination, in contradiction with the simplest unification model.