The introduction of mammography screening programs has significantly reduced breast cancer mortality rates. Nevertheless, some lesions remain undetected, especially in dense breast tissue. Studies have shown that phase-contrast imaging can improve breast cancer diagnosis by increasing soft tissue contrast. Furthermore, grating-based phase-contrast imaging enables the simultaneous acquisition of absorption-, phase-contrast, and scattering, so-called dark-field images. The latter allows the classification of microcalcifications. In addition, breast computed tomography (BCT) systems can identify and discriminate overlapping but clinically relevant structures. This study investigates the benefit of combining grating-based phase-contrast with BCT. For this task, two Photon counting detector (PCD)s are used, and their performance is compared to a flat panel detector in terms of their resolution. The results demonstrate a resolution advantage of PCDs over flat panel detectors. Furthermore, we explore the potential of grating-based phase-contrast breast computed tomography (gbpc-BCT) with a breast phantom and a freshly dissected fibroadenoma. Improved image contrast could be achieved with radiation doses comparable to those used inclinical mammography.