The emergence of large language models (LLMs), pre-trained on massive datasets, has demonstrated strong performance across a wide range of natural language processing (NLP) tasks, including text classification. While prior studies have examined the use of LLMs for predicting the intent of user feedback and reported encouraging results, these investigations remain limited in scope. Furthermore, the vast volume of feedback posted daily, particularly for popular applications, combined with the computational and financial overhead of commercial LLMs, renders large-scale deployment impractical. In contrast, smaller models provide greater efficiency and lower cost but generally at the expense of reduced accuracy. In this paper, we aim to balance accuracy and efficiency in feedback classification. We first present a comprehensive study of zero-shot classification using four widely adopted LLMs, GPT-3.5-Turbo, GPT-4o, Flan-T5, and Llama3-70B, on diverse feedback datasets collected from multiple platforms, including app stores, forums, and X, which are categorized under different schemes. This analysis reveals how classification scheme design and platform characteristics influence the predictive performance of LLMs. Building on these insights, we propose a two-tier routing strategy for scalable app store feedback classification. In this approach, low-complexity instances are processed by lightweight fine-tuned models, while ambiguous cases are routed to high-capacity LLMs for more reliable decisions. Experimental results show that this strategy retains 98.4% to 100.4% of zero-shot LLM accuracy while reducing request and token costs by 67.8% and 66.3%, respectively.