In-room imaging is a prerequisite for adaptive proton therapy. The use of onboard cone-beam computed tomography (CBCT) imaging, which is routinely acquired for patient position verification, can enable daily dose reconstructions and plan adaptation decisions. Image quality deficiencies though, hamper dose calculation accuracy and make corrections of CBCTs a necessity. This study compared three methods to correct CBCTs and create synthetic CTs that are suitable for proton dose calculations. CBCTs, planning CTs and repeated CTs (rCT) from 33 H&N cancer patients were used to compare a deep convolutional neural network (DCNN), deformable image registration (DIR) and an analytical image-based correction method (AIC) for synthetic CT (sCT) generation. Image quality of sCTs was evaluated by comparison with a same-day rCT, using mean absolute error (MAE), mean error (ME), Dice similarity coefficient (DSC), structural non-uniformity (SNU) and signal/contrast-to-noise ratios (SNR/CNR) as metrics. Dosimetric accuracy was investigated in an intracranial setting by performing gamma analysis and calculating range shifts. Neural network-based sCTs resulted in the lowest MAE and ME (37/2 HU) and the highest DSC (0.96). While DIR and AIC generated images with a MAE of 44/77 HU, a ME of -8/1 HU and a DSC of 0.94/0.90. Gamma and range shift analysis showed almost no dosimetric difference between DCNN and DIR based sCTs. The lower image quality of AIC based sCTs affected dosimetric accuracy and resulted in lower pass ratios and higher range shifts. Patient-specific differences highlighted the advantages and disadvantages of each method. For the set of patients, the DCNN created synthetic CTs with the highest image quality. Accurate proton dose calculations were achieved by both DCNN and DIR based sCTs. The AIC method resulted in lower image quality and dose calculation accuracy was reduced compared to the other methods.