In mobile applications, it is crucial to provide intuitive means for 2D and 3D interaction. A large number of techniques exist to support a natural user interface (NUI) by detecting the user's hand posture in RGB+D (depth) data. Depending on the given interaction scenario and its environmental properties, each technique has its advantages and disadvantages regarding accuracy and the robustness of posture detection. While the interaction environment in a desktop setup can be constrained to meet certain requirements, a handheld scenario has to deal with varying environmental conditions. To evaluate the performance of techniques on a mobile device, a powerful software framework was developed that is capable of processing and fusing RGB and depth data directly on a handheld device. Using this framework, five existing hand posture recognition techniques were integrated and systematically evaluated by comparing their accuracy under varying illumination and background. Overall results reveal best recognition rate of posture detection for combined RGB+D data at the expense of update rate. To support users in choosing the appropriate technique for their specific mobile interaction task, we derived guidelines based on our study. In the last step, an experimental study was conducted using the detected hand postures to perform the canonical 3D interaction tasks selection and positioning in a mixed reality handheld setup.