The information systems engineering community is increasingly exploring the use of Large Language Models (LLMs) for a variety of tasks, including domain modeling, business process modeling, software modeling, and systems modeling. However, most existing research remains exploratory and lacks a systematic approach to analyzing the impact of prompt content on model quality. This paper seeks to fill this gap by investigating how different levels of description granularity (whole text vs. paragraph-by-paragraph) and modeling strategies (model-based vs. list-based) affect the quality of LLM-generated domain models. Specifically, we conducted an experiment with two state-of-the-art LLMs (GPT-4o and Llama-3.1-70b-versatile) on tasks involving use case and class modeling. Our results reveal challenges that extend beyond the chosen granularity, strategy, and LLM, emphasizing the importance of human modelers not only in crafting effective prompts but also in identifying and addressing critical aspects of LLM-generated models that require refinement and correction.