Patient dose optimisation in computed tomography (CT) should be done using clinically relevant tasks when dealing with image quality assessments. In the present work, low-contrast detectability for an average patient morphology was assessed on 56 CT units, using a model observer applied on images acquired with two specific protocols of an anthropomorphic phantom containing spheres. Images were assessed using the channelised Hotelling observer (CHO) with dense difference of Gaussian channels. The results were computed by performing receiver operating characteristics analysis (ROC) and using the area under the ROC curve (AUC) as a figure of merit. The results showed a small disparity at a volume computed tomography dose index (CTDIvol) of 15 mGy depending on the CT units for the chosen image quality criterion. For 8-mm targets, AUCs were 0.999 ± 0.018 at 20 Hounsfield units (HU) and 0.927 ± 0.054 at 10 HU. For 5-mm targets, AUCs were 0.947 ± 0.059 and 0.702 ± 0.068 at 20 and 10 HU, respectively. The robustness of the CHO opens the way for CT protocol benchmarking and optimisation processes.