Objective.Proton therapy administers a highly conformal dose to the tumour region, necessitating accurate prediction of the patient's 3D map of proton relative stopping power (RSP) compared to water. This remains challenging due to inaccuracies inherent in single-energy computed tomography (SECT) calibration. Recent advancements in spectral x-ray CT (xCT) and proton CT (pCT) have shown improved RSP estimation compared to traditional SECT methods. This study aims to provide the first comparison of the imaging and RSP estimation performance among dual-energy CT (DECT) and photon-counting CT (PCCT) scanners, and a pCT system prototype.Approach.Two phantoms were scanned with the three systems for their performance characterisation: a plastic phantom, filled with water and containing four plastic inserts and a wood insert, and a heterogeneous biological phantom, containing a formalin-stabilised bovine specimen. RSP maps were generated by converting CT numbers to RSP using a calibration based on low- and high-energy xCT images, while pCT utilised a distance-driven filtered back projection algorithm for RSP reconstruction. Spatial resolution, noise, and RSP accuracy were compared across the resulting images.Main results.All three systems exhibited similar spatial resolution of around 0.54 lp/mm for the plastic phantom. The PCCT images were less noisy than the DECT images at the same dose level. The lowest mean absolute percentage error (MAPE) of RSP,(0.28±0.07)%, was obtained with the pCT system, compared to MAPE values of(0.51±0.08)%and(0.80±0.08)%for the DECT- and PCCT-based methods, respectively. For the biological phantom, the xCT-based methods resulted in higher RSP values in most of the voxels compared to pCT.Significance.The pCT system yielded the most accurate estimation of RSP values for the plastic materials, and was thus used to benchmark the xCT calibration performance on the biological phantom. This study underlined the potential benefits and constraints of utilising such a novelex-vivophantom for inter-centre surveys in future.