Understanding forest health is of great importance for the conservation of the integrity of forest ecosystems. The monitoring of forest health is, therefore, indispensable for the long-term conservation of forests and their sustainable management. In this regard, evaluating the amount and quality of dead wood is of utmost interest as they are favorable indicators of biodiversity. Apparently, remote sensing-based machine learning techniques have proven to be more efficient and sustainable with unprecedented accuracy in forest inventory. However, the application of these techniques is still in its infancy with respect to dead wood mapping. This study investigates for the first time the automatic classification of individual coniferous trees into five decay stages (live, declining, dead, loose bark, and clean) from combined airborne laser scanning (ALS) point clouds and CIR images using three Machine Learning methods - 3D point cloud-based deep learning (PointNet), Convolutional Neural Network (CNN), and Random Forest (RF). All models achieved promising results, reaching overall accuracy (OA) up to 90.9%, 90.6%, and 80.6% for CNN, RF, and PointNet, respectively. The experimental results reveal that the image-based approach notably outperformed the 3D point cloud-based one, while spectral image texture is of the highest relevance to the success of categorizing tree decay. Our models could therefore be used for automatic determination of single tree decay stages and landscape-wide assessment of dead wood amount and quality using modern airborne remote sensing techniques with machine/deep learning. The proposed method can contribute as an important and rigorous tool for monitoring biodiversity in forest ecosystems.