Nowadays, location-aware devices, such as GPS, provide a huge volume of spatial-temporal data. Analyzing the data to understand the behavior of objects (e.g. people) could be beneficial in many application areas. Due to the spatial and temporal nature and their complexity, researchers have developed various data mining techniques such as trajectory segmentation, which splits the trajectories into sub-trajectories, to prepare them for the mining step. A central issue in discovering knowledge is choosing an appropriate trajectory segmentation technique. In this paper, we provide a comparative study on two trajectory segmentation techniques, density-based and grid-based, when applied to sequential patterns discovery. We conducted experiments using two real-life datasets to evaluate the performance of the methods in terms of execution time and their impact on discovering the sequential patterns. The experimental results showed that the density-based is more efficient, while the grid-based is more effective.