We compare high angular resolution mid-infrared (mid-IR) and Atacama Large Millimeter/submillimeter Array (ALMA) far-infrared (far-IR) images of twelve nearby (median 21 Mpc) Seyfert galaxies selected from the Galaxy Activity, Torus, and Outflow Survey (GATOS). The mid-IR unresolved emission contributes more than 60% of the nuclear (diameters of 1.5″ ∼ 150 pc) emission in most galaxies. By contrast, the ALMA 870 μm continuum emission is mostlyresolved with a median diameter of 42 pc and typically along the equatorial direction of the torus (Paper I). The Eddington ratios and nuclear hydrogen column densities (NH) of half the sample are favorable to launching polar and/or equatorial dusty winds, according to numerical simulations. Six of these show mid-IR extended emission approximately in the polar direction as traced by the narrow line region and perpendicular to the ALMA emission. In a few galaxies, the nuclear NH might be too high to uplift large quantities of dusty material along the polar direction. Five galaxies have low NH and/or Eddington ratios and thus polar dusty winds are not likely. We generated new radiative transfer CAT3D-WIND disk+wind models and model images at 8, 12, and 700 μm. We tailored these models to the properties of the GATOS Seyferts in this work. At low wind-to-disk cloud ratios, the far-IR model images have disk- and ring-like morphologies. The characteristic "X"-shape associated with dusty winds is seen better in the far-IR at intermediate-high inclinations for the extended-wind configurations. In most of the explored models, the mid-IR emission mainly comes from the inner part of the disk and cone. Extended biconical and one-sided polar mid-IR emission is seen in extended-wind configurations and high wind-to-disk cloud ratios. When convolved to the typical angular resolution of our observations, the CAT3D-WIND model images reproduce qualitative aspects of the observed mid- and far-IR morphologies. However, low to intermediate values of the wind-to-disk ratio are required to account for the observed large fractions of unresolved mid-IR emission in our sample. This work and Paper I provide observational support for the torus+wind scenario. The wind component is more relevant at high Eddington ratios and/or active galactic nucleus luminosities, and polar dust emission is predicted at nuclear column densities of up to ∼1024 cm−2. The torus or disk component, on the other hand, prevails at low luminosities and/or Eddington ratios.