As Large Language Models (LLMs) increasingly integrate into everyday workflows, where users shape outcomes through multi-turn collaboration, a critical question emerges: do users with different personality traits systematically prefer certain LLMs over others? We conduc-ted a study with 32 participants evenly distributed across four Keirsey personality types, evaluating their interactions with GPT-4 and Claude 3.5 across four collaborative tasks: data analysis, creative writing, information retrieval, and writing assistance. Results revealed significant personality-driven preferences: Rationals strongly preferred GPT-4, particularly for goal-oriented tasks, while idealists favored Claude 3.5, especially for creative and analytical tasks. Other personality types showed task-dependent preferences. Sentiment analysis of qualitative feedback confirmed these patterns. Notably, aggregate helpfulness ratings were similar across models, showing how personality-based analysis reveals LLM differences that traditional evaluations miss.