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Smartwatches and smartphones contain accelerometers and gyroscopes that sense a user's movements, and can help identify the activity a user is performing. Research into smartphone-based activity recognition has exploded over the past few years, but research into smartwatch-based activity recognition is still in its infancy. In this paper we compare smartwatch and smartphone-based activity recognition, and smartwatches are shown to be capable of identifying specialized hand-based activities, such as eating activities, which cannot be effectively recognized using a smartphone (e.g., smartwatches can identify the "drinking" activity with 93.3% accuracy while smartphones achieve an accuracy of only 77.3%). Smartwatch-based activity recognition can form the basis of new biomedical and health applications, including applications that automatically track a user's eating habits.