This workshop paper presents a critical examination of the integration of Generative AI (Gen AI) into the academic writing process, focusing on the use of AI as a collaborative tool. It contrasts the performance and interaction of two AI models, Gemini and ChatGPT, through a collaborative inquiry approach where researchers engage in facilitated sessions to design prompts that elicit specific AI responses for crafting research outlines. This case study highlights the importance of prompt design, output analysis, and recognizing the AI's limitations to ensure responsible and effective AI integration in scholarly work. Preliminary findings suggest that prompt variation significantly affects output quality and reveals distinct capabilities and constraints of each model. The paper contributes to the field of Human-Computer Interaction by exploring effective prompt strategies and providing a comparative analysis of Gen AI models, ultimately aiming to enhance AI-assisted academic writing and prompt a deeper dialogue within the HCI community.