Next-generation wireless networks require massive connectivity and ubiquitous coverage, for which non-terrestrial networks (NTNs) are a promising enabler. However, NTNs, especially non-geostationary satellites bring about challenges such as increased handovers (HOs) due to the moving coverage area of the satellite on the ground. Accordingly, in this work, we compare the conventional measurement-based HO triggering mechanism with other alternatives such as distance, elevation angle, and timer-based methods in terms of the numbers of HOs, ping-pong HOs, and radio link failures. The system-level simulations, carried out in accordance with the 3GPP model, show that the measurement-based approach can outperform the other alternatives provided that appropriate values of hysteresis/offset margins and time-to-trigger parameters are used. Moreover, future directions regarding this work are also provided at the end.