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 coding of point clouds despite their underlying similarities. In this work, we present UH-PCC, a unified hierarchical model for point cloud compression, that synergizes Octree-based and Feature-based coding under a single model with shared parameters via a Hierarchical Feature Coding (HFC) framework. The HFC is a conditional coder operating level-wise, supported by a novel hierarchical hyperprior model that eliminates the need for additional side-information. We also utilize a style control mechanism that enables fine-grain rate control without separate model parameters for different bitrates and allows seamless switching between inter- and intra-modes. Our proposal exhibits performance on par with the state-of-the-art methods.