Context. The advent of 8−10 m class telescopes for the first time makes it possible to compare in detail quasars with similar luminosity and very different redshifts. Aims. We conducted a search for z-dependent gradients in line-emission diagnostics and derived physical properties by comparing, in a narrow bolometric luminosity range (log L ∼ 46.1± 0.4 [erg s −1 ]), some of the most luminous local z < 0.6 quasars with some of the lowest luminosity sources yet found at redshift z = 2.1−2.5. Methods. Moderate signal-to-noise ratio spectra for 22 high-redshift sources were obtained with the 10.4 m Gran Telescopio Canarias (GTC), for which the HST (largely the Faint Object Spectrograph) archive provides a low-redshift control sample. We compared the spectra in the context of the 4D Eigenvector 1 formalism, meaning that we divided both source samples into highly accreting population A and population B sources accreting at a lower rate. Results. Civλ1549, the strongest and most reliable diagnostic line, shows very similar properties at both redshifts, which confirms the Civλ1549 profile differences at high redshift between populations A and B, which are well established in local quasars. The Civλ1549 blueshift that appears quasi-ubiquitous in higher L sources is found in only half (population A) of the quasars observed in the two samples. A Civλ1549 evolutionary Baldwin effect is certainly disfavored. We find evidence for lower metallicity in the GTC sample that may point toward a gradient with z. No evidence for a gradient in M BH or L/L Edd is found. Conclusions. Spectroscopic differences established at low z are also present in much higher redshift quasars. Our results on the Civλ1549 blueshift suggest that it depends both on source luminosity and L/L Edd . Given that our samples involve sources with very similar luminosity, the evidence for a systematic metallicity decrease, if real, points toward an evolutionary effect. Our samples are not large enough to effectively constrain possible changes of M BH or L/L Edd with redshift. The two samples appear representative of a slowly evolving quasar population that is most likely present at all redshifts.