Recent investigations show that large language models (LLMs), specifically GPT-4, not only have remarkable capabilities in common Natural Language Processing (NLP) tasks but also exhibit human-level performance on various professional and academic benchmarks. However, whether GPT-4 can be directly used in practical applications and replace traditional artificial intelligence (AI) tools in specialized domains requires further experimental validation. In this paper, we explore the potential of LLMs such as GPT-4 to outperform traditional AI tools in dementia diagnosis. Comprehensive comparisons between GPT-4 and traditional AI tools are conducted to examine their diagnostic accuracy in a clinical setting. Experimental results on two real clinical datasets show that, although LLMs like GPT-4 demonstrate potential for future advancements in dementia diagnosis, they currently do not surpass the performance of traditional AI tools. The interpretability and faithfulness of GPT-4 are also evaluated by comparison with real doctors. We discuss the limitations of GPT-4 in its current state and propose future research directions to enhance GPT-4 in dementia diagnosis.