We compute the virial mass (M) of the central black hole and the luminosity‐to‐mass (L/M) ratio of ≈300 low‐z quasars and luminous type 1 Seyfert nuclei. We analyse the following: (1) whether radio‐quiet and radio‐loud objects show systematic differences in terms of M and L/M; (2) the influence of M and L/M on the shape of the Hβ broad component line profile; and (3) the significance of the so‐called ‘blue outliers’, i.e. sources showing a significant blueshift of the [O iii]λλ4959,5007 lines with respect to the narrow component of Hβ, which is used as an estimator of the quasar reference frame. We show that M and L/M distributions for radio‐quiet and radio‐loud sources are probably different for samples matched in luminosity and redshift, in the sense that radio‐quiet sources have systematically smaller masses and larger L/M. However, the L/M ratio distributions become indistinguishable if 8.5 < log M < 9.5. Line profile comparisons for median spectra computed over narrow ranges of M and L/M indicate that a Lorentz function provides a better fit for higher L/M sources and a double Gaussian for lower L/M values. A second (redshifted) Gaussian component at low L/M appears as a red asymmetry frequently observed in radio‐loud and radio‐quiet sources with broader (full width at half‐maximum ≳4000 km s−1) Hβ broad component profiles. This component becomes stronger in larger mass and lower L/M sources. No specific influence of radio loudness on the Hβ broad component profile is detected, although equivalent widths of Hβ broad component and especially of [O iii]λλ4959,5007 are larger for radio‐loud sources. We identify five more ‘blue outlier’ sources. Since these sources are, on average, one magnitude brighter than other active galactic nuclei with similar mass, their resulting Eddington ratio is 2–3 times higher. We hint at evolutionary effects that explain some of these results, and reinforce the ‘eigenvector 1’ correlations.