Airborne laser scanning (ALS) data has been widely used for total aboveground tree biomass (AGB) modelling, however, there is less research focusing on estimating specific tree biomass components (wood, branches, bark, and foliage). Knowledge about these biomass components is essential for carbon accounting, understanding forest nutrient cycling, and other applications. In this study, we compare additive AGB estimation (sum of estimated components) with direct AGB estimation using deep neural network (DNN) and random forest (RF) models. We utilise two point cloud DNNs: point-based Dynamic Graph Convolutional Neural Network (DGCNN) and Octree-based Convolutional Neural Network (OCNN). DNN and RF models were trained using a dataset comprised of 2336 sample plots from a mixed temperate forest in New Brunswick, Canada. Results indicate that additive AGB models perform similarly to direct models in terms of coefficient of determination (R2) and rootmean square error (RMSE), and reduced the mean absolute percentage error (MAPE) by 22% on average. Compared to RF, the DNNs provided a small improvement in performance, with OCNN explaining 5% more variation in the data (R2 = 0.76) and reducing MAPE by 20% on average. Overall, this study showcases the effectiveness of additive tree AGB models and highlights the potential of DNNs for enhanced AGB estimation. To further improve DNN performance, we recommend using larger training datasets, implementing hyperparameter optimization, and incorporating additional data such as multispectral imagery.