Marine heatwave (MHW) characteristics - such as frequency, intensity and duration - are increasing, largely due to global warming. However, while corresponding marine cold spell (MCS) characteristics have decreased over most regions, importantly, concomitant changes in MHW and MCS characteristics remain unclear. Here, we provide a comparative global assessment of these changes based on satellite sea surface temperature (SST) observations over 1982-2020. Across the planet, we find distinct differences in mean MHW and MCS metrics. Furthermore, decreasing trends in MCS characteristics are not necessarily aligned with increasing trends in MHW characteristics. While differences in intensity trends are mainly explained by SST variance trends, differences in exposure trends are less clear. Overall, decreasing MCS exposure and intensities are found to be largely driven by warming SST, rather than changes to SST variance, so it is expected that MCS will continue to diminish in their frequency, intensity and duration under global warming.