Screening patients for enrollment is a well-known, labor-intensive bottleneck that leads to under-enrollment and, ultimately, trial failures. Recent breakthroughs in large language models (LLMs) offer a promising opportunity to use artificial intelligence to improve screening. This study systematically explored both encoder- and decoder-based generative LLMs for screening clinical narratives to facilitate clinical trial recruitment. We examined both general-purpose LLMs and medical-adapted LLMs and explored three strategies to alleviate the "Lost in the Middle" issue when handling long documents, including 1) Original long-context: using the default context windows of LLMs, 2) NER-based extractive summarization: converting the long document into summarizations using named entity recognition, 3) RAG: dynamic evidence retrieval based on eligibility criteria. The 2018 N2C2 Track 1 benchmark dataset is used for evaluation. Our experimental results show that the MedGemma model with the RAG strategy achieved the best micro-F1 score of 89.05%, outperforming other models. Generative LLMs have remarkably improved trial criteria that require long-term reasoning across long documents, whereas trial criteria that span a short piece of context (e.g., lab tests) show incremental improvements. The real-world adoption of LLMs for trial recruitment must consider specific criteria for selecting among rule-based queries, encoder-based LLMs, and generative LLMs to maximize efficiency within reasonable computing costs.