Context. The high-fidelity solar spectral atlas prepared by Delbouille et al. (Liège atlas, 1973) and the atlas by Neckel (Hamburg atlas, 1999, Sol. Phys., 184, 421) are widely recognised as the most important collection of reference spectra of the Sun at disc centre in the visible wavelength range. The two datasets serve as fundamental resources for many researchers, in particular for chemical abundance analyses. But despite their similar published specifications (spectral resolution and noise level), the shapes of the spectral lines in the two atlases differ significantly and systematically. Aims: Knowledge of any instrumental degradations is imperative to fully exploit the information content of spectroscopic data. We seek to investigate the magnitude of these differences and explain the possible sources. We provide the wavelength-dependent correction parameters that need to be taken into account when the spectra are to be compared with synthetic data, for instance. Methods: A parametrically degraded version of the Hamburg spectrum was fitted to the Liège spectrum. The parameters of the model (wavelength shift, broadening, intensity scaling, and intensity offset) represent the different characteristics of the respective instruments, observational strategies, and data processing. Results: The wavelength scales of the Liège and Hamburg atlases differ on average by 0.5 mÅ with a standard deviation of ± 2 mÅ, except for a peculiar region around 5500 Å. The continuum levels are offset by up to 18% below 5000 Å, but remain stably at a 0.8% difference towards the red. We find no evidence for spectral stray light in the Liège spectrum. Its resolving power is almost independent of wavelength but limited to about 216 000, which is between two to six times lower than specified. When accounting for the degradations determined in this work, the spectra of the two atlases agree to within a few parts in 103. The fit parameters displayed in Fig. 2 and derived data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/590/A118