Both augmented and virtual reality (AR and VR) devices have been widely adopted in industries and for personal usages. Doctors can now use VR devices to perform pathological assessments. In addition to traditional input devices such as handheld controllers, advanced input techniques such as ray-casting (RC) and hand gesture manipulation (HGM) have been developed. However, comparisons of the performance of these techniques have not been reported. The objectives of this study were to test the hypotheses that using the RC technique is more time-consuming and more difficult than using HGM and that object shape is a significant factor affecting both the time to complete the task and rating of difficulty. Thirty participants joined an experiment. They wore a Microsoft HoloLens 2 headpiece to perform the virtual object transferring tasks. The results show that the movement time using RC was significantly longer than that (9987.8 ms vs. 4840.3 ms, p < 0.001) of using HGM. The rating of difficulty of RC was also significantly higher than that of HGM (2.56 vs. 1.51, $p_{\mathrm{Holm}}<0.001$). Details of the effects of the interaction method and object shape, together with the considerations of gender and movement direction, were discussed. In addition, two movement time models were developed. The R² values of these models show that the fitness of both models is adequate. However, the prediction error of the integrated model is relatively higher than that of the HGM-specific one due to the volatile nature of the RC tasks. This study is novel in providing scientific data to compare the performance of an AR device using RC and HGM, which will contribute to the advancement of AR technology.