\textbf{Objective:}\newline Sharing behavioral health and wearable data poses privacy challenges, as traditional de-identification remains vulnerable to re-identification. Differential privacy (DP) provides mathematical guarantees through a tunable privacy budget, $\varepsilon$⁠. This study evaluates the feasibility of generating and releasing DP synthetic behavioral health data with high analytical utility, identifying practical $\varepsilon$ values for public data sharing.\newline\newline \textbf{Materials and methods:}\newline We analyzed physiological data from wearable devices and self-reported data from Phase 1 of the Lived Experiences Measured Using Rings Study (LEMURS), which tracked sleep, stress, and well-being among first-year college students. Three DP synthetic data generators: AIM, MST, and PATECTGAN, were evaluated across privacy budgets ranging from $\varepsilon=1$ to 100. Utility was assessed using L1/L2 errors, correlation, regression, UMAP, and assessed vulnerability via privacy attacks.\newline\newline \textbf{Results}\newline AIM outperformed MST and PATECTGAN in preserving both statistical and analytical properties of the original data. For the Survey dataset, the lowest marginal errors occurred at $\varepsilon=5$ and 10. Correlation, regression, and UMAP analyses confirmed that AIM-generated data closely replicated original relationships at moderate $\varepsilon$ values.\newline\newline \textbf{Discussion}\newline Choice of privacy budget is still an open question, and it is task-agnostic and dataset-specific. Moderate privacy budgets (⁠$5 \le \varepsilon \le 10$) maintained key associations between physiological and psychological measures while ensuring privacy. AIM’s workload-aware design effectively allocated noise toward relevant features, enhancing performance.\newline\newline \textbf{Conclusion:}\newline A privacy budget of $\varepsilon = 5$ offers a practical balance between data utility and participant privacy for LEMURS behavioral health data sharing.