Device heterogeneity poses major challenges in Federated Learning (FL), where resource-constrained clients slow down synchronous schemes that wait for all updates before aggregation. Asynchronous FL addresses this by incorporating updates as they arrive, substantially improving efficiency. While its efficiency gains are well recognized, its privacy costs remain largely unexplored, particularly for high-end devices that contribute updates more frequently, increasing their cumulative privacy exposure. This paper presents the first comprehensive analysis of the efficiency-fairness-privacy trade-off in synchronous vs. asynchronous FL under realistic device heterogeneity. We empirically compare FedAvg and staleness-aware FedAsync using a physical testbed of five edge devices spanning diverse hardware tiers, integrating Local Differential Privacy (LDP) and the Moments Accountant to quantify per-client privacy loss. Using Speech Emotion Recognition (SER) as a privacy-critical benchmark, we show that FedAsync achieves up to 10x faster convergence but exacerbates fairness and privacy disparities: high-end devices contribute 6-10x more updates and incur up to 5x higher privacy loss, while low-end devices suffer amplified accuracy degradation due to infrequent, stale, and noise-perturbed updates. These findings motivate the need for adaptive FL protocols that jointly optimize aggregation and privacy mechanisms based on client capacity and participation dynamics, moving beyond static, one-size-fits-all solutions.