This paper contributes to the growing body of work that aims to characterize similarities and differences between synchrophasor data from real-power systems and those from synthetic power systems with emulated Phasor Measurement Units (PMUs). In particular, we survey previous works that characterize PMU noise and analyze the impacts on applications of these time-series data into machine learning algorithms in the power systems domain. We benchmark these methodologies with three datasets: data from an Oregon State University local PMU network, from two PMUs using the same set of sensors, and from multiple-utility interconnect-wide data. We found that it is important to consider each signal individually when synthesizing PMU data with noise, and that the noise needs to be adjusted by key statistical metrics.