Background: Studies have shown the potential adverse health effects, ranging from headaches to cardiovascular disease, associated with long-term negative emotions and chronic stress. Since many indicators of stress are imperceptible to observers, the early detection and intervention of stress remains a pressing medical need. Physiological signals offer a non-invasive method of monitoring emotions and are easily collected by smartwatches. Existing research primarily focuses on developing generalized machine learning-based models for emotion classification. Objective: We aim to study the differences between personalized and generalized machine learning models for three-class emotion classification (neutral, stress, and amusement) using wearable biosignal data. Methods: We developed a convolutional encoder for the three-class emotion classification problem using data from WESAD, a multimodal dataset with physiological signals for 15 subjects. We compared the results between a subject-exclusive generalized, subject-inclusive generalized, and personalized model. Results: For the three-class classification problem, our personalized model achieved an average accuracy of 95.06% and F1-score of 91.71, our subject-inclusive generalized model achieved an average accuracy of 66.95% and F1-score of 42.50, and our subject-exclusive generalized model achieved an average accuracy of 67.65% and F1-score of 43.05. Conclusions: Our results emphasize the need for increased research in personalized emotion recognition models given that they outperform generalized models in certain contexts. We also demonstrate that personalized machine learning models for emotion classification are viable and can achieve high performance.