We present new mid-infrared imaging data for three Type-1 Seyfert galaxies obtained with T-ReCS on the Gemini-South Telescope at subarcsecond resolution. Our aim is to enlarge the sample studied in a previous work to compare the properties of Type-1 and Type-2 Seyfert tori using clumpy torus models and a Bayesian approach to fit the infrared (IR) nuclear spectral energy distributions. Thus, the sample considered here comprises 7 Type-1, 11 Type-2, and 3 intermediate-type Seyferts. The unresolved IR emission of the Seyfert 1 galaxies can be reproduced by a combination of dust heated by the central engine and direct active galactic nucleus (AGN) emission, while for the Seyfert 2 nuclei only dust emission is considered. These dusty tori have physical sizes smaller than 6 pc radius, as derived from our fits. Unification schemes of AGN 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 Type-1 and Type-2 Seyfert 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 a direct view of the AGN, and vice versa. In our sample, Seyfert 2 tori have larger covering factors (CT = 0.95 ± 0.02) and smaller escape probabilities (P esc = 0.05% ± 0.08 0.03%) than those of Seyfert 1 (CT = 0.5 ± 0.1; P esc = 18% ± 3%). All the previous differences are significant according to the Kullback-Leibler divergence. Thus, on the basis of the results presented here, the classification of a Seyfert galaxy as a Type-1 or Type-2 depends more on the intrinsic properties of the torus rather than on its mere inclination toward us, in contradiction with the simplest unification model.