Conversational Recommender Systems (CRSs) deliver personalised recommendations through multi-turn natural language dialogue and increasingly support both task-oriented and exploratory interactions. Yet, the factors shaping user interaction preferences remain underexplored. In this within-subjects study (\(N = 139\)), participants experienced two scripted CRS dialogues, rated their experiences, and indicated the importance of eight system qualities. Logistic regression revealed that preference for the exploratory interaction was predicted by enjoyment, usefulness, novelty, and conversational quality. Unexpectedly, perceived effectiveness was also associated with exploratory preference. Clustering uncovered five latent user profiles with distinct dialogue style preferences. Moderation analyses indicated that age, gender, and control preference significantly influenced these choices. These findings integrate affective, cognitive, and trait-level predictors into CRS user modelling and inform autonomy-sensitive, value-adaptive dialogue design. The proposed predictive and adaptive framework applies broadly to conversational AI systems seeking to align dynamically with evolving user needs.