Multimodal remote sensing data, including spectral and lidar or photogrammetry, is crucial for achieving satisfactory land-use / land-cover classification results in urban scenes. So far, most studies have been conducted in a 2D context. When 3D information is available in the dataset, it is typically integrated with the 2D data by rasterizing the 3D data into 2D formats. Although this method yields satisfactory classification results, it falls short in fully exploiting the potential of 3D data by restricting the model's ability to learn 3D spatial features directly from raw point clouds. Additionally, it limits the generation of 3D predictions, as the dimensionality of the input data has been reduced. In this study, we propose a fully 3D-based method that fuses all modalities within the 3D point cloud and employs a dedicated dual-branch Transformer model to simultaneously learn geometric and spectral features. To enhance the fusion process, we introduce a cross-attention-based mechanism that fully operates on 3D points, effectively integrating features from various modalities across multiple scales. The purpose of cross-attention is to allow one modality to assess the importance of another by weighing the relevant features. We evaluated our method by comparing it against both 3D and 2D methods using the 2018 IEEE GRSS Data Fusion Contest (DFC2018) dataset. Our findings indicate that 3D fusion delivers competitive results compared to 2D methods and offers more flexibility by providing 3D predictions. These predictions can be projected onto 2D maps, a capability that is not feasible in reverse. Additionally, we evaluated our method on different datasets, specifically the ISPRS Vaihingen 3D and the IEEE 2019 Data Fusion Contest. Our code will be published here: https://github.com/aldinorizaldy/hyperpointformer.