LiDAR-based roadside perception is a cornerstone of advanced Intelligent Transportation Systems (ITS). While considerable research has addressed optimal LiDAR placement for infrastructure, the profound impact of differing LiDAR scanning patterns on perceptual performance remains comparatively under-investigated. The inherent nature of various scanning modes - such as traditional repetitive (mechanical/solid-state) versus emerging non-repetitive (e.g. prism-based) systems - leads to distinct point cloud distributions at varying distances, critically dictating the efficacy of object detection and overall environmental understanding. To systematically investigate these differences in infrastructure-based contexts, we introduce the "InfraLiDARs' Benchmark," a novel dataset meticulously collected in the CARLA simulation environment using concurrently operating infrastructure-based LiDARs exhibiting both scanning paradigms. Leveraging this benchmark, we conduct a comprehensive statistical analysis of the respective LiDAR scanning abilities and evaluate the impact of these distinct patterns on the performance of various leading 3D object detection algorithms. Our findings reveal that non-repetitive scanning LiDAR and the 128-line repetitive LiDAR were found to exhibit comparable detection performance across various scenarios. Despite non-repetitive LiDAR's limited perception range, it's a cost-effective option considering its low price. Ultimately, this study provides insights for setting up roadside perception system with optimal LiDAR scanning patterns and compatible algorithms for diverse roadside applications, and publicly releases the "InfraLiDARs' Benchmark" dataset to foster further research.