We present mid-infrared (MIR; 7.5-13.5 μm) imaging and spectroscopy observations obtained with the CanariCam (CC) instrument on the 10.4-m Gran Telescopio CANARIAS for a sample of 20 nearby, MIR bright and X-ray luminous quasi-stellar objects (QSOs). We find that for the majority of QSOs the MIR emission is unresolved at angular scales ∼0.3 arcsec, corresponding to physical scales ≲600 pc. We find that the higher-spatial resolution CC spectra have similar shapes to those obtained with Spitzer/IRS, and hence we can assume that the spectra are not heavily contaminated by extended emission in the host galaxy. We thus take advantage of the higher signal-to-noise ratio Spitzer/IRS spectra, as a fair representation of the nuclear emission, to decompose it into a combination of active galactic nuclei (AGN), polycyclic aromatic hydrocarbon (PAH) and stellar components. In most cases, the AGN is the dominant component, with a median contribution of 85 per cent of the continuum light at MIR (5-15 μm) within the IRS slit. This IR AGN emission is well reproduced by clumpy torus models. We find evidence for significant differences in the parameters that describe the dusty tori of QSOs when compared with the same parameters of Seyfert 1 and 2 nuclei. In particular, we find a lower number of clouds (N0 ≲ 12), steeper radial distribution of clouds (q ∼ 1.5-3.0) and clouds that are less optically thick (τV ≲ 100) than in Seyfert 1, which could be attributed to dusty structures that have been partially evaporated and piled up by the higher radiation field in QSOs. We find that the combination of the angular width σtorus, viewing angle i, and number of clouds along the equatorial line, N0, produces large escape probabilities (Pesc > 2 per cent) and low geometrical covering factors (f2 ≲ 0.6), as expected for AGN with broad lines in their optical spectra.