Seamless streaming of high quality video under unstable network condition is a big challenge. HTTP adaptive streaming (HAS) provides a solution that adapts the video quality according to the network conditions. Traditionally, HAS algorithm runs at the client side while the clients are unaware of bottlenecks in the radio channel and competing clients. The traditional adaptation strategies do not explicitly coordinate between the clients, servers, and cellular networks. The lack of coordination has been shown to lead to suboptimal user experience. As a response, multi-access edge computing (MEC)-assisted adaptation techniques emerged to take advantage of computing and content storage capabilities in mobile networks. In this study, we investigate the performance of both MEC-assisted and client-side adaptation methods in a multi-client cellular environment. Evaluation and comparison are performed in terms of not only the video rate and dynamics of the playback buffer but also the fairness and bandwidth utilization. We conduct extensive experiments to evaluate the algorithms under varying client, server, dataset, and network settings. Results demonstrate that the MEC-assisted algorithms improve fairness and bandwidth utilization compared to the client-based algorithms for most settings. They also reveal that the buffer-based algorithms achieve significant quality of experience; however, these algorithms perform poorly compared with throughput-based algorithms in protecting the playback buffer under rapidly varying bandwidth fluctuations. In addition, we observe that the preparation of the representation sets affects the performance of the algorithms, as does the playback buffer size and segment duration. Finally, we provide suggestions based on the behaviors of the algorithms in a multi-client environment.