Context: The advent of Large Language Models (LLMs) is transforming software development, significantly enhancing software engineering (SE) processes. Research has explored their role within development teams, focusing on the specific purposes for which LLMs are used within SE tasks, such as artifact generation, decision-making support, and information retrieval. Despite the growing body of work on LLMs in SE, most studies have centered on broad adoption trends, neglecting the nuanced relationship between individual cognitive and behavioral factors and their impact on purpose-specific adoption. While factors such as perceived effort and performance expectancy have been explored at a general level, their influence on distinct SE purposes remains underexamined. This gap hinders the development of tailored LLM-based systems (e.g., Generative AI Agents) that align with engineers' specific needs and limits the ability of team leaders to devise effective strategies for fostering LLM adoption in targeted workflows. Objectives: For the reasons mentioned above, this study aims to study the individual factors that drive the choice to use LLMs for distinct SE purposes. Methods: To achieve the above-mentioned objective, we surveyed 188 software engineers to test the relationship between individual attributes related to technology adoption and LLM adoption across five key purposes, using structural equation modeling (SEM). The Unified Theory of Acceptance and Use of Technology (UTAUT2) was applied to characterize individual adoption behaviors. Results: The findings reveal that purpose-specific adoption is influenced by distinct factors, some of which negatively impact adoption when considered in isolation, underscoring the complexity of LLM integration in SE.