The next generations of mobile communications should deal with a set of new use cases, leading to a higher demand for spectral efficiency. Full‐duplex (FD) arises as a promising technology since it has the potential to double the system capacity without additional spectrum. However, FD networks are hindered by self‐interference (SI) and co‐channel interference caused by the reuse of frequency resources. Therefore, radio resource allocation (RRA) in FD networks by means of user pairing, frequency assignment, and power allocation are of utmost importance in order to improve spectral/energy efficiency and ensure quality of service (QoS). Although previous works investigated RRA to improve spectral efficiency, the fundamental question of where adaptive power allocation should be employed in the uplink and/or downlink of FD networks in a cost‐effective way remains unanswered. This article addresses this question in the context of total data rate maximization with QoS constraints where we propose four optimization problems using different power allocation strategies. The branch and bound method is employed to optimally solve the four formulated problems, which were used as upper bound solutions for benchmarking purposes. Moreover, we propose a low computational complexity solution able to adaptively switch the power allocation strategy depending on the scenario. Detailed system‐level simulations indicate that the best node to employ adaptive power allocation (mobile terminal or base station) depends on the cell radius and SI level. Also, our results show that, compared to existing solutions, the proposed low‐complexity is a great and intelligent strategy in terms of system performance and computational complexity considering both perfect and imperfect channel state information. We propose four optimization problems using different power allocation strategies to solve the total data rate maximization problem with minimum rate constraints in full‐duplex systems. Motivated by the high computational complexity to obtain the optimal solutions of the investigated problems, we propose a heuristic solution with lower computational complexity. The proposed solution presents good performance in terms of outage rate and spectral efficiency when the performance/complexity trade‐off is assessed.