Point cloud compression is a critical component in 3D vision systems utilizing point cloud data to represent the physical world. Existing works on point cloud compression separately tackle Octree-based and Feature-based compression of point clouds despite their underlying similarities. In this work, we present UniFHiD: a unified fully hierarchical model for dynamic point cloud compression, that synergizes Octree and Feature Coding under a single model with shared parameters. The key enabler in this unification is the aligned feature extraction between the two coding methods. Particularly, we propose a novel Conditional Feature Coding framework that non-trivially gives rise to hierarchical Feature coding and hierarchical Inter Coding by utilizing a novel conditional encoder design along with a hierarchical hyperprior model for entropy modeling. We also utilize a style control mechanism that enables fine-grain rate control without separate model parameters for each target bitrate range and allows seamless switching between inter- and intra-mode for dynamic and static compression. Our proposal exhibits performance on par with the state-of-the-art methods.