Human Activity Recognition (HAR) is one of the important applications of digital health that helps to track fitness or to avoid sedentary behavior by monitoring daily activities. Due to the growing popularity of consumer wearable devices, smartwatches, and earbuds are being widely adopted for HAR applications. However, using just one of the devices may not be sufficient to track all activities properly. This paper proposes a multi-modal approach to HAR by using both buds and watch. Using a large dataset of 44 subjects collected from both in-lab and in-home environments, we demonstrate the limitations of using a single modality as well as the importance of a multi-modal approach. Moreover, we also train and evaluate the performance of five different machine learning classifiers for various combinations of devices such as buds only, watch only, and both. We believe the detailed analyses presented in this paper may serve as a benchmark for the research community to explore and build upon in the future.