In wireless access networks, one of the most recent challenges is reducing the power consumption of the network, while preserving the quality of service perceived by users. Hence, mobile operators are rethinking their network design by considering two objectives, namely, saving power and guaranteeing a satisfactory quality of service. Since these objectives are conflicting, a tradeoff becomes inevitable. We formulate a multi-objective optimization with aims of minimizing the network power consumption and transmission delay. Power saving is achieved by adjusting the operation mode of the network base stations from high transmit power levels to low transmit levels or even sleep mode. Minimizing the transmission delay is achieved by selecting the best user association with the network base stations. In this article, we cover two different technologies: IEEE 802.11 and LTE. Our formulation captures the specificity of each technology in terms of the power model and radio resource allocation. After exploring typical multi-objective approaches, we resort to a weighted sum mixed integer linear program. This enables us to efficiently tune the impact of the power and delay objectives. We provide extensive simulations for various preference settings that enable to assess the tradeoff between power and delay in IEEE 802.11WLANs and LTE networks. We show that for a power minimization setting, aWLAN consumes up to 16%less power than legacy solutions. A thorough analysis of the optimization results reveals the impact of the network topology, particularly the inter-cell distance, on both objectives. For an LTE network, we assess the impact of urban, rural and realistic deployments on the achievable tradeoffs. The power savings mainly depend on user distribution and the power consumption of the sleep mode. Compared with legacy solutions, we obtained power savings of up to 22.3% in a realistic LTE networks. When adequately tuned, our optimization approach reduces the transmission delay by up to 6% in a WLAN and 8% in an LTE network.