Video/audio conferencing systems have been used extensively for remote collaboration over many years. Recently, virtual and mixed reality (VR/MR) systems have started to show great potential as communication media for remote collaboration. Prior studies revealed that the creation of common ground between discourse participants is crucial for collaboration and that grounding techniques change with the communication medium. However, it is difficult to find previous research that compares VR and MR communication system performances with video conferencing systems regarding the creation of common ground for collaborative problem solving. On the other hand, prior studies have found that display fidelity and interaction fidelity had significant effects on performance-intensive individual tasks in virtual reality. Fidelity in VR can be defined as the degree of objective accuracy with which the real-world is represented by the virtual world. However, to date, fidelity for collaborative tasks in VR/MR has not been defined or studied much. In this paper, we compare five different communication media for the establishment of common ground in collaborative problem-solving tasks: Webcam, headband camera, VR, MR, and audio-only conferencing systems. We analyzed these communication media with respect to collaborative fidelity components which we defined. For the experiments, we utilized two different types of collaborative tasks: a 2D Tangram puzzle and a 3D Soma cube puzzle. The experimental results show that the traditional Webcam performed better than the other media in the 2D task, while the headband camera performed better in the 3D task. In terms of collaboration fidelity, these results were somehow predictable, although there was a little difference between our expectations and the results.