Conventional thoracic 4DCBCT scans take 1320 projections over 4 min. This paper investigates which reconstruction algorithms best leverage Respiratory-Motion-Guided (RMG) acquisition in order to reduce scan time and dose while maintaining image quality. We investigated a 200 projection, on average 1 min RMG acquisition. RMG acquisition ensures even angular separation between projections at each respiratory phase by adjusting the imaging gantry rotation to the patient respiratory signal in real time. Conventional 1320 projection data and RMG 200 projection data were simulated from 4DCT volumes of 14 patients. Each patient had an initial 4DCT reconstruction, treated as a planning 4DCT, and a 4DCT reconstruction acquired later, used for 4DCBCT data simulation and evaluation. Reconstructions were computed using the Feldkamp-David-Kress (FDK), McKinnon-Bates (MKB), RecOnstructiOn using Spatial and TEmporal Regularization (ROOSTER), and Motion Compensated FDK (MCFDK) algorithms. We also introduced and evaluated a novel MCMKB algorithm. Image quality was evaluated with Root-Mean-Square Error (RMSE), Structural SIMilarity index (SSIM) and Tissue Interface Sharpness (TIS). Rigid registration of the tumor volume regions between the reconstruction and the ground truth was used to evaluate geometric accuracy. Relative to conventional 4DCBCT acquisition, the RMG acquisition delivered 80% less dose and was on average 70% faster. The conventional-acquisition 4DFDK-reconstruction volumes had mean RMSE, SSIM, TIS and geometric error of 94, 0.9987, 2.69 and 1.19 mm respectively. The RMG-acquisition MCFDK-reconstruction volumes had mean RMSE, SSIM, TIS and geometric error of 113, 0.9986, 1.76 and 1.77 mm respectively with minimal increase in computational cost. These results suggest scan time and dose can be significantly reduced with minimal impact on reconstruction quality by implementing RMG acquisition and motion compensated reconstruction.