Purpose: To compare the efficacy of CT-on-rails versus in-room CBCT for daily adaptive proton therapy. Methods: We analyzed a cohort of ten head-and-neck patients with daily CBCT and corresponding virtual CT images. The necessity of moving the patient after a CT scan is the most significant difference in the adaptation workflow, leading to an increased treatment execution uncertainty σ. It is a combination of the isocenter-matching σ_i and random patient movements induced by the couch motion σ_m. The former is assumed to never exceed 1 mm. For the latter, we studied three different scenarios with σ_m = 1, 2, and 3 mm. Accordingly, to mimic the adaptation workflow with CT-on-rails, we introduced random offsets after Monte-Carlo-based adaptation but before delivery of the adapted plan. Results: There were no significant differences in accumulated dose-volume histograms and dose distributions for σ_m = 1 and 2 mm. Offsets with σ_m = 3 mm resulted in underdosage to CTV and hot spots of considerable volume. Conclusion: Since σ_m typically does not exceed 2 mm for in-room CT, there is no clinically significant dosimetric difference between the two modalities for online adaptive therapy of head-and-neck patients. Therefore, in-room CT-on-rails can be considered a good alternative to CBCT for adaptive proton therapy