In this study we compared the image quality of a synchrotron radiation (SR) breast computed tomography (BCT) system with a clinical BCT in terms of contrast-to-noise ratio (CNR), signal-to-noise ratio (SNR), noise power spectrum (NPS), spatial resolution and detail visibility. A breast phantom consisting of several slabs of breast-adipose equivalent material with different embedded targets (i.e., masses, fibers and calcifications) was used. Phantom images were acquired using a dedicated BCT system installed at the Radboud University Medical Center (Nijmegen, The Netherlands) and the SR BCT system at the SYRMEP beamline of Elettra SR facility (Trieste, Italy) based on a photon-counting detector. Images with the SR setup were acquired mimicking the clinical BCT conditions (i.e., energy of 30 keV and radiation dose of 6.5 mGy). Images were reconstructed with an isotropic cubic voxel of 273 µm for the clinical BCT, while for the SR setup two phase-retrieval (PhR) kernels (referred to as "smooth" and "sharp") were alternatively applied to each projection before tomographic reconstruction, with voxel size of 57 × 57 × 50 µm3. The CNR for the clinical BCT system can be up to 2-times higher than SR system, while the SNR can be 3-times lower than SR system, when the smooth PhR is used. The peak frequency of the NPS for the SR BCT is 2 to 4-times higher (0.9 mm-1 and 1.4 mm-1 with smooth and sharp PhR, respectively) than the clinical BCT (0.4 mm-1). The spatial resolution (MTF10%) was estimated to be 1.3 lp/mm for the clinical BCT, and 5.0 lp/mm and 6.7 lp/mm for the SR BCT with the smooth and sharp PhR, respectively. The smallest fiber visible in the SR BCT has a diameter of 0.15 mm, while for the clinical BCT is 0.41 mm. Calcification clusters with diameter of 0.13 mm are visible in the SR BCT, while the smallest diameter for the clinical BCT is 0.29 mm. As expected, the image quality of the SR BCT outperforms the clinical BCT system, providing images with higher spatial resolution and SNR, and with finer granularity. Nevertheless, this study assesses the image quality gap quantitatively, giving indications on the benefits associated with SR BCT and providing a benchmarking basis for its clinical implementation. In addition, SR-based studies can provide a gold-standard in terms of achievable image quality, constituting an upper-limit to the potential clinical development of a given technique.