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Voice activity and overlapped speech detection (respectively VAD and OSD) are key pre-processing tasks for speaker diarization. The final segmentation performance highly relies on the robustness of these sub-tasks. Recent studies have shown VAD and OSD can be trained jointly using a multi-class classification model. However, these works are often restricted to a specific speech domain, lacking information about the generalization capacities of the systems. This paper proposes a complete and new benchmark of different VAD and OSD models, on multiple audio setups (single/multi-channel) and speech domains (e.g. media, meeting...). Our 2/3-class systems, which combine a Temporal Convolutional Network with speech representations adapted to the setup, outperform state-of-the-art results. We show that the joint training of these two tasks offers similar performances in terms of F1-score to two dedicated VAD and OSD systems while reducing the training cost. This unique architecture can also be used for single and multichannel speech processing.