Next-generation automotive radars provide elevation data in addition to range-, azimuth-and Doppler velocity. In this experimental study, we apply a state-of-the-art object detector (PointPillars), previously used for LiDAR 3D data, to such 3+1D radar data (where 1D refers to Doppler). In ablation studies, we first explore the benefits of the additional elevation information, together with that of Doppler, radar cross section and temporal accumulation, in the context of multi-class road user detection. We subsequently compare object detection performance on the radar and LiDAR point clouds, object class-wise and as a function of distance. To facilitate our experimental study, we present the novel View-of-Delft (VoD) automotive dataset. It contains 8693 frames of synchronized and calibrated 64-layer LiDAR-, (stereo) camera-, and 3+1D radar-data acquired in complex, urban traffic. It consists of 123106 3D bounding box annotations of both moving and static objects, including 26587 pedestrian, 10800 cyclist and 26949 car labels. Our results show that object detection on 64-layer LiDAR data still outperforms that on 3+1D radar data, but the addition of elevation information and integration of successive radar scans helps close the gap. The VoD dataset is made freely available for scientific benchmarking at https://intelligent-vehicles.org/datasets/view-ofdelft/.