3D Gaussian Splatting (3DGS) data compression is crucial for enabling efficient storage and transmission in 3D scene modeling. However, its development remains limited due to inadequate entropy models and suboptimal quantization strategies for both lossless and lossy compression scenarios, where existing methods have yet to 1) fully leverage hyperprior information to construct robust conditional entropy models, and 2) apply fine-grained, element-wise quantization strategies for improved compression granularity. In this work, we propose a novel Mixture of Priors (MoP) strategy to simultaneously address these two challenges. Specifically, inspired by the Mixture-of-Experts (MoE) paradigm, our MoP approach processes hyperprior information through multiple lightweight MLPs to generate diverse prior features, which are subsequently integrated into the MoP feature via a gating mechanism. To enhance lossless compression, the resulting MoP feature is utilized as a hyperprior to improve conditional entropy modeling. Meanwhile, for lossy compression, we employ the MoP feature as guidance information in an element-wise quantization procedure, leveraging a prior-guided Coarse-to-Fine Quantization (C2FQ) strategy with a predefined quantization step value. Specifically, we expand the quantization step value into a matrix and adaptively refine it from coarse to fine granularity, guided by the MoP feature, thereby obtaining a quantization step matrix that facilitates element-wise quantization. Extensive experiments demonstrate that our proposed 3DGS data compression framework achieves state-of-the-art performance across multiple benchmarks, including Mip-NeRF360, BungeeNeRF, DeepBlending, and Tank&Temples.