Because they are both Apple products, the browser that works smoothest with Macintosh OS X is:

The browser that works smoothest with Macintosh OS X is Safari. This is primarily because Safari is developed by Apple specifically for its operating systems, including macOS. As a native application, Safari is optimized to integrate seamlessly with OS X, taking full advantage of the underlying technologies and features of the operating system. This results in better performance, increased stability, and enhanced power efficiency when compared to third-party browsers.

Additionally, Safari often receives updates aligned with macOS updates, ensuring compatibility and access to the latest features and security enhancements. It also provides a user interface that is consistent with the overall look and feel of macOS, contributing to a more coherent user experience.

While other browsers like Firefox, Chrome, and Edge can run on macOS, they might not be as finely tuned for the system as Safari, which is deeply embedded into the Apple ecosystem.