Transformers have excelled in natural language processing and computer vision, paving their way to sensor-based Human Activity Recognition (HAR). Previous studies show that transformers outperform their counterparts exclusively when they harness abundant data or employ compute-intensive optimization algorithms. However, neither of these scenarios is viable in sensor-based HAR due to the scarcity of data in this field and the frequent need to perform training and inference on resource-constrained devices. Our extensive investigation into various implementations of transformer-based versus non-transformer-based HAR using wearable sensors, encompassing more than 500 experiments, corroborates these concerns. We observe that transformer-based solutions pose higher computational demands, consistently yield inferior performance, and experience significant performance degradation when quantized to accommodate resource-constrained devices. Additionally, transformers demonstrate lower robustness to adversarial attacks, posing a potential threat to user trust in HAR.