Recent years have witnessed a significant increase in the adoption of AI techniques to enhance electronic design automation. In particular, the emergence of Large Language Models (LLMs) has sparked significant interest in LLM-assisted hardware design generation, spanning applications from classical digital circuits to quantum computing. Despite substantial progress in this direction, the quality of LLM-generated hardware design still cannot meet the requirements for practical deployment. In this work, we identify three critical challenges hindering the development of LLM-assisted hardware design generation: 1) limited data availability, 2) varied data quality, 3) inadequate inference-time efficiency. To address these fundamental challenges, this paper introduces a two-stage framework for AI-assisted hardware design by exploring decentralized training and personalized inference. In the first stage, we propose to harness private domain design sources through a hierarchical decentralized training mechanism that addresses data-sharing constraints. To mitigate the impact of low-quality data, we identify optimization opportunities in hardware generation tasks, using user-defined metrics for model aggregation. The second stage focuses on client personalization to enhance both speed and quality. We introduce a new metric, Trueput, to analyze LLM-assisted hardware generation efficiency. To optimize Trueput, we implement personalized inference-time acceleration and customized sampling strategies. Evaluating both classical and quantum benchmarks, our experimental results demonstrate that the proposed two-stage framework can significantly improve the model capability for hardware design generation. As orthogonal enhancements to existing methods, our framework can achieve $33\% \sim 50\%$ semantic accuracy improvement and $2.3$ times speedup, depending on the difficulty of the generation tasks.