The detection of blueshifted absorption lines likely associated with ionized iron K-shell transitions in the X-ray spectra of many active galactic nuclei (AGNs) suggests the presence of a highly ionized gas outflowing with mildly relativistic velocities (0.03c-0.6c) named ultra-fast outflow (UFO). Within the SUBWAYS project, we characterized these winds starting from a sample of 22 radio-quiet quasars at an intermediate redshift (0.1<=z<=0.4) and compared the results with similar studies in the literature on samples of local Seyfert galaxies (i.e., 42 radio-quiet AGNs observed with XMM-Newton at z<=0.1) and high redshift radio-quiet quasars (i.e., 14 AGNs observed with XMM-Newton and Chandra at z>=1.4). The scope of our work is a statistical study of UFO parameters and incidence considering the key physical properties of the sources, such as supermassive black hole (SMBH) mass, bolometric luminosity, accretion rates, and spectral energy distribution (SED) with the aim of gaining new insights into the UFO launching mechanisms. We find indications that highly luminous AGNs with a steeper X-ray/UV ratio, alpha_ox, are more likely to host UFOs. The presence of UFOs is not significantly related to any other AGN property in our sample. These findings suggest that the UFO phenomenon may be transient. Focusing on AGNs with UFOs, other important findings from this work include: (1) faster UFOs have larger ionization parameters and column densities; (2) X-ray radiation plays a more crucial role in driving highly ionized winds compared to UV; (3) the correlation between outflow velocity and luminosity is significantly flatter than what is expected for radiatively driven winds; (4) more massive black holes experience higher wind mass losses, suppressing the accretion of matter onto the black hole; (5) the UFO launching radius is positively correlated with the Eddington ratio. Furthermore, our analysis suggests the involvement of multiple launching mechanisms, including radiation pressure and magneto-hydrodynamic processes, rather than pointing to a single, universally applicable mechanism.