Quantifying synchronization phenomena based on the timing of events has recently attracted a great deal of interest in various disciplines such as neuroscience or climatology. A multitude of similarity measures has been proposed for this purpose, including event synchronization (ES) and event coincidence analysis (ECA) as two widely applicable examples. While ES defines synchrony in a data-adaptive local way that does not distinguish between different timescales, ECA requires selecting a specific scale for analysis. In this paper, we use slightly modified versions of both ES and ECA that address previous issues with respect to proper normalization and boundary treatment, which are particularly relevant for short time series with low temporal resolution. By numerically studying threshold crossing events in coupled autoregressive processes, we identify a practical limitation of ES when attempting to study synchrony between serially dependent event sequences exhibiting event clustering in time. Practical implications of this observation are demonstrated for the case of functional network representations of climate extremes based on both ES and ECA, while no marked differences between both measures are observed for the case of epileptic electroencephalogram data. Our findings suggest that careful event detection along with diligent preprocessing is recommended when applying ES while less crucial for ECA. Despite the lack of a general modus operandi for both event definition and detection of synchronization, we suggest ECA as a widely robust method, especially for time-resolved synchronization analyses of event time series from various disciplines.