We have recently built and characterized the performance of a monolithic scintillator detector based on a 32 mm × 32 mm × 22 mm LYSO:Ce crystal read out by digital silicon photomultiplier (dSiPM) arrays coupled to the crystal front and back surfaces in a dual-sided readout (DSR) configuration. The detector spatial resolution appeared to be markedly better than that of a detector consisting of the same crystal with conventional back-sided readout (BSR). Here, we aim to evaluate the influence of this difference in the detector spatial response on the quality of reconstructed images, so as to quantify the potential benefit of the DSR approach for high-resolution, whole-body time-of-flight (TOF) positron emission tomography (PET) applications. We perform Monte Carlo simulations of clinical PET systems based on BSR and DSR detectors, using the results of our detector characterization experiments to model the detector spatial responses. We subsequently quantify the improvement in image quality obtained with DSR compared to BSR, using clinically relevant metrics such as the contrast recovery coefficient (CRC) and the area under the localized receiver operating characteristic curve (ALROC). Finally, we compare the results with simulated rings of pixelated detectors with DOI capability. Our results show that the DSR detector produces significantly higher CRC and increased ALROC values than the BSR detector. The comparison with pixelated systems indicates that one would need to choose a crystal size of 3.2 mm with three DOI layers to match the performance of the BSR detector, while a pixel size of 1.3 mm with three DOI layers would be required to get on par with the DSR detector.