The recent emergence of multimodal large language models (LLMs) has introduced new opportunities for improving visual hazard recognition on construction sites. Unlike traditional computer vision models that rely on domain-specific training and extensive datasets, modern LLMs can interpret and describe complex visual scenes using simple natural language prompts. However, despite growing interest in their applications, there has been limited investigation into how different LLMs perform in safety-critical visual tasks within the construction domain. To address this gap, this study conducts a comparative evaluation of five state-of-the-art LLMs: Claude-3 Opus, GPT-4.5, GPT-4o, GPT-o3, and Gemini 2.0 Pro, to assess their ability to identify potential hazards from real-world construction images. Each model was tested under three prompting strategies: zero-shot, few-shot, and chain-of-thought (CoT). Zero-shot prompting involved minimal instruction, few-shot incorporated basic safety context and a hazard source mnemonic, and CoT provided step-by-step reasoning examples to scaffold model thinking. Quantitative analysis was performed using precision, recall, and F1-score metrics across all conditions. Results reveal that prompting strategy significantly influenced performance, with CoT prompting consistently producing higher accuracy across models. Additionally, LLM performance varied under different conditions, with GPT-4.5 and GPT-o3 outperforming others in most settings. The findings also demonstrate the critical role of prompt design in enhancing the accuracy and consistency of multimodal LLMs for construction safety applications. This study offers actionable insights into the integration of prompt engineering and LLMs for practical hazard recognition, contributing to the development of more reliable AI-assisted safety systems.