LiDAR model selection is a critical issue in roadside sensing systems, as it directly determines both perception capability and deployment cost. However, the lack of empirical benchmarks for comparing perception performance across different LiDAR configurations has greatly constrained scientific sensor selection and deployment planning. To address this gap, we present MR-LiDAR, a controlled multi-resolution LiDAR benchmark for roadside perception diagnostics. Using 16-, 32-, 80-, and 128-beam LiDARs in identical roadside scenarios, we collect point clouds and ground-truth annotations for diverse traffic participants, including vehicles and vulnerable road users (VRUs), across varying distances. This controlled design isolates intrinsic LiDAR specifications, particularly beam count and beam distribution, as the key variables for precise performance diagnostics. Based on MR-LiDAR, we conduct systematic empirical analyses to examine how beam count, beam distribution, target distance, object category, and vehicle occlusion affect LiDAR perception performance. The results reveal that all of these factors have substantial impacts. In particular, contrary to the common assumption that higher beam counts always yield better perception, we show that an 80-beam LiDAR with optimized beam distribution can match or even outperform a 128-beam LiDAR with uniform beam distribution. In addition, we provide a practical reference guide for LiDAR selection, including target point-count statistics and detection performance comparisons based on two widely used detection algorithms. This work offers a diagnostic benchmark and practical guidance for determining cost-effective LiDAR configurations in roadside perception applications.