Reliable early detection of Alzheimer's disease (AD) is challenging, particularly due to the limited availability of labeled data. While large language models (LLMs) have shown strong transfer capabilities across do mains, adapting them to the AD domain through supervised fine-tuning remains largely unexplored. In this work, we empirically evaluate various model architectures across three heterogeneous transcript corpora (Pitt, CCC, ADRC) to investigate their effectiveness for text-based AD detection and analyze how task-relevant information is encoded within their internal representations. To the best of our knowledge, our fine-tuned BERT and T5 models establish a new state-of-the-art on the Pitt and CCC datasets, while achieving strong performance on ADRC. In parallel, the decoder-only Llama-1B achieves highly competitive results comparable to BERT and T5 across all three corpora, highlighting its effectiveness for AD detection. We further conduct a comprehensive evaluation of the Llama-1B backbone, analyzing cross-corpus transferability, optimal input chunk-size granularity, and the impact of clinical transcript markers. Also, we use linear probing to empirically show that fine-tuning shifts the representations of individual tokens, both linguistic markers and content words, in ways that reflect AD-related signal.