Stellar population synthesis (SPS) models are invaluable to study star clusters and galaxies. They provide means to extract stellar masses, stellar ages, star formation histories, chemical enrichment and dust content of galaxies from their integrated spectral energy distributions, colours or spectra. As most models, they contain uncertainties which can hamper our ability to model and interpret observed spectra. This work aims at studying a specific source of model uncertainty: the choice of an empirical vs. a synthetic stellar spectral library. Empirical libraries suffer from limited coverage of parameter space, while synthetic libraries suffer from modelling inaccuracies. Given our current inability to have both ideal stellar-parameter coverage with ideal stellar spectra, what should one favour: better coverage of the parameters (synthetic library) or better spectra on a star-by-star basis (empirical library)? To study this question, we build a synthetic stellar library mimicking the coverage of an empirical library, and SPS models with different choices of stellar library tailored to these investigations. Through the comparison of model predictions and the spectral fitting of a sample of nearby galaxies, we learned that: predicted colours are more affected by the coverage effect than the choice of a synthetic vs. empirical library; the effects on predicted spectral indices are multiple and defy simple conclusions; derived galaxy ages are virtually unaffected by the choice of the library, but are underestimated when SPS models with limited parameter coverage are used; metallicities are robust against limited HRD coverage, but are underestimated when using synthetic libraries.