eleworking became a vastly popular practice lately owing to the Covid-19 outbreak. Our present study aims to evaluate the operating energy consumption in 5G versus Wifi6 networks for this remote working case study. We specifically study the detailed operations of transmission and reception at both radio access networks and quantify their power consumption in the downlink, analytically, using simulations and, for the case of Wifi6. We focus on three case studies in the framework of a teleworking tool: audio session, video session and shared screen session. Our results show that for the use case of video session in the downlink, when the number of users is rather small, Wifi6 consumes less power, however, as the number of users gets larger, 5G with Multi-User MIMO (MU-MIMO) outperforms the individual Wifi accesses. These results depend on the number of simultaneous MUMIMO streams as well as on the fixed component of the power consumption of the 5G, for which we present a sensitivity analysis as well.