In a data-centric era, concerns regarding privacy and ethical data handling grow as machine learning relies more on personal information. This empirical study investigates the privacy, generalization, and stability of deep learning models in the presence of additive noise in federated learning frameworks. Our main objective is to provide strategies to measure the generalization, stability, and privacy-preserving capabilities of these models and further improve them. To this end, five noise infusion mechanisms at varying noise levels within centralized and federated learning settings are explored. As model complexity is a key component of the generalization and stability of deep learning models during training and evaluation, a comparative analysis of three Convolutional Neural Network (CNN) architectures is provided. The paper introduces Signal-to-Noise Ratio (SNR) as a quantitative measure of the trade-off between privacy and training accuracy of noise-infused models, aiming to find the noise level that yields optimal privacy and accuracy. Moreover, the Price of Stability and Price of Anarchy are defined in the context of privacy-preserving deep learning, contributing to the systematic investigation of the noise infusion strategies to enhance privacy without compromising performance. Our research sheds light on the delicate balance between these critical factors, fostering a deeper understanding of the implications of noise-based regularization in machine learning. By leveraging noise as a tool for regularization and privacy enhancement, we aim to contribute to the development of robust, privacy-aware algorithms, ensuring that AI-driven solutions prioritize both utility and privacy.