Point cloud registration is an extensively studied field in computer vision, featuring a variety of existing methods, all aimed at achieving the common objective of determining a transformation that aligns two point clouds. Methods like the Iterative Closet Point (ICP) and Fast Global Registration (FGR) have shown to work well for many years, but recent work has explored different learning-based approaches, showing promising results. This work compares the performance of two learning-based methods GeoTransformer and RegFormer against three baseline methods ICP point-to-point, ICP point-to-plane, and FGR. The comparison was conducted on data provided by the Swedish Defence Research Agency (FOI), where the data was captured with a photon-counting LiDAR sensor. Findings suggest that while ICP point-to-point and ICP point-to-plane exhibit solid performance, the GeoTransformer demonstrates the potential for superior outcomes. Additionally, the RegFormer and FGR perform worse than the ICP variants and the GeoTransformer.