Traffic prediction is fundamental to intelligent transportation systems and urban computing, yet many cities continue to suffer from traffic data scarcity due to limited sensor deployment and uneven urban development. Cross-city knowledge transfer has thus attracted increasing attention, enabling data-rich cities to assist data-scarce ones. However, centralized approaches raise privacy concerns, while existing federated methods struggle with pronounced spatiotemporal heterogeneity across cities. To address these challenges, we propose MoE-FedTP, a personalized federated cross-city spatiotemporal prediction framework based on lightweight Mixture-of-Experts (MoE) networks. MoE-FedTP first employs spatiotemporal neural networks to extract features from both source and target cities, then introduces a set of expert networks derived from different source cities through partial parameter sharing. A gating mechanism dynamically fuses the experts to capture diverse traffic dynamics, achieving fine-grained modeling of urban heterogeneity while preserving privacy. Experiments on four real-world traffic datasets show that MoE-FedTP consistently outperforms state-of-the-art cross-city and federated learning baselines, demonstrating its effectiveness in enhancing prediction accuracy for data-scarce cities.