Recent developments and the beginning market introduction of high-resolution imaging 4D (3+1D) radar sensors have initialized deep learning-based radar perception research. We investigate deep learning-based models operating on radar point clouds for 3D object detection. 3D object detection on lidar point cloud data is a mature area of 3D vision. Many different architectures have been proposed, each with strengths and weaknesses. Due to similarities between 3D lidar point clouds and 3+1D radar point clouds, those existing 3D object detectors are a natural basis to start deep learning-based 3D object detection on radar data. Thus, the first step is to analyze the detection performance of the existing models on the new data modality and evaluate them in depth. In order to apply existing 3D point cloud object detectors developed for lidar point clouds to the radar domain, they need to be adapted first. While some detectors, such as PointPillars, have already been adapted to be applicable to radar data, we have adapted others, e.g., Voxel R-CNN, SECOND, PointRCNN, and PV-RCNN. To this end, we conduct a cross-model validation (evaluating a set of models on one particular data set) as well as a cross-data set validation (evaluating all models in the model set on several data sets). The high-resolution radar data used are the View-of-Delft and Astyx data sets. Finally, we evaluate several adaptations of the models and their training procedures. We also discuss major factors influencing the detection performance on radar data and propose possible solutions indicating potential future research avenues.