What makes an interaction with the LLM more preferable for the user? While it is intuitive to assume that information accuracy in the LLM's responses would be one of the influential variables, recent studies have found that inaccurate LLM's responses could still be preferable when they are perceived to be more authoritative, certain, well-articulated, or simply verbose. These variables interestingly fall under the broader category of language style, implying that the style in the LLM's responses might meaningfully influence users' preferences. This hypothesized dynamic could have double-edged consequences: enhancing the overall user experience while simultaneously increasing their susceptibility to risks such as LLM's misinformation or hallucinations. In this short paper, we present our preliminary studies in exploring this subject. Through a series of exploratory and experimental user studies, we found that LLM's language style does indeed influence user's preferences, but how and which language styles influence the preference varied across different user populations, and more interestingly, moderated by the user's very own individual traits. As a preliminary work, the findings in our studies should be interpreted with caution, particularly given the limitations in our samples, which still need wider demographic diversity and larger sample sizes. Our future directions will first aim to address these limitations, which would enable a more comprehensive joint effect analysis between the language style, individual traits, and preferences, and further investigate the potential causal relationship between and beyond these variables.