As a hyper-natural interaction technique in 3D user interfaces, non-isomorphic rotation has been considered an effective approach for rotation tasks, where a static or dynamic control-display gain can be applied to amplify or attenuate a rotation. However, it is not clear whether non-isomorphic rotation can benefit 6-degree-of-freedom (6-DOF) manipulation tasks in AR and VR. In this paper, we extended the usability studies of non-isomorphic rotation from rotation-only tasks to 6-DOF manipulation tasks and analyzed the collected data using a 2-component model. Using a mixed reality (MR) simulation approach, we also investigated whether environment (AR or VR) had an impact on 3D manipulation tasks. The results reveal that although both static and dynamic non-isomorphic rotation techniques could save time and effort in ballistic phases, only dynamic non-isomorphic rotation was significantly faster than isomorphic rotation. Interestingly, while environment had no significant impact on overall user performance, we found evidence that it could affect fine-tuning in correction phases. We also found that most participants preferred AR over VR, indicating that environmental visual realism could be helpful to improve user experience.