We analyze the power-delay trade-off in a Network-on-Chip (NoC) under three Dynamic Voltage and Frequency Scaling (DVFS) policies. The first rate-based policy sets frequency and voltage of the NoC to the minimum value that allows to sustain the injection rate without reaching saturation. The second queue-based policy uses a feedback-loop approach to throttle the NoC frequency and voltage such that the average backlog of the injection queues tracks a target value. The third delay-based policy uses a closed-loop strategy that targets a given NoC end-to-end average delay. We first show that, despite the different mechanism and implementation, both rate-based and queue-based policies obtain very similar results in terms of power and delay, and we propose a theoretical interpretation of this similarity. Then, we show that delay-based policy generally offers a better power-delay trade-off. We obtained our results with an extensive set of experiments on synthetic traffic, as well as multimedia, communications and PARSEC benchmarks. For all the experiments, we report both cycle-accurate simulation results for the analysis of NoC delay and accurate power results obtained targeting a standard-cell library in an advanced 28-nm FDSOI CMOS technology.