In densely populated urban areas, the increasing variability of power supply and demand due to the presence of a multitude of prosumers will greatly affect power quality (PQ). In order to monitor the state of distribution systems, a larger number of Phasor Measurement Units (PMU) is expected to be deployed in the next future. However, to what extent PMU algorithms (especially those used in P Class instruments) can actually detect typical PQ events and can replace or integrate existing PQ meters is still unclear. The goal of this paper is to investigate this issue and to provide a preliminary overview of the role of PMUs for voltage dips and swells detection. The proposed analysis relies on a simulation-based performance comparison between two PMU algorithms (provided with an additional median filter) and the classic technique relying on zero-crossing detection and true Root Mean Square (RMS) magnitude estimation. All simulations have been performed in realistic conditions, assuming to acquire voltage waveforms compliant with the EN Standard 50160:2010 and affected by dips or swells of different amplitude and duration. Even if no experimental data are collected on the field, the proposed analysis provides a useful insight into the potentialities and limitations of PMU algorithms for voltage dips and swells detection.