In the context of rapid urbanization, monitoring the evolution of cities is crucial. To do so, 3D change detection and characterization is of capital importance since, unlike 2D images, 3D data contain vertical information of utmost importance to monitoring city evolution (that occurs along both horizontal and vertical axes). Urban 3D change detection has thus received growing attention, and various methods have been published on the topic. Nevertheless, no quantitative comparison on a public dataset has been reported yet. This study presents an experimental comparison of six methods: three traditional (difference of DSMs, C2C and M3C2), one machine learning with hand-crafted features (a random forest model with a stability feature) and two deep learning (feed-forward and Siamese architectures). In order to compare these methods, we prepared five sub-datasets containing simulated pairs of 3D annotated point clouds with different characteristics: from high to low resolution, with various levels of noise. The methods have been tested on each sub-dataset for binary and multi-class segmentation. For supervised methods, we also assessed the transfer learning capacity and the influence of the training set size. The methods we used provide various kinds of results (2D pixels, 2D patches or 3D points), and each of them is impacted by the resolution of the PCs. However, while the performances of deep learning methods highly depend on the size of the training set, they seem to be less impacted by training on datasets with different characteristics. Oppositely, conventional machine learning methods exhibit stable results, even with smaller training sets, but embed low transfer learning capacities. While the main changes in our datasets were usually identified, there were still numerous instances of false detection, especially in dense urban areas, thereby calling for further development in this field. To assist such developments, we provide a public dataset composed of pairs of point clouds with different qualities together with their change-related annotations. This dataset was built with an original simulation tool which allows one to generate bi-temporal urban point clouds under various conditions.