1. Installation and package management: Homebrew is a package manager for macOS that allows users to easily install, update, and manage software packages. It uses a simple command line interface and installs packages into standard locations. On the other hand, Nix is a purely functional package manager that is available for multiple operating systems. It uses a unique approach of isolating packages in their own environments, ensuring reproducibility and conflict-free installation.

2. Package availability: Homebrew provides a large number of packages from its main repository, known as Homebrew Core. It also allows users to tap into additional repositories, called taps, that offer even more packages. Nix, on the other hand, has a curated set of packages available in its main repository, known as Nixpkgs. However, Nix also allows users to define their own package sets and share them with others, giving it a high level of flexibility.

3. Version management: Homebrew allows users to easily switch between different versions of a package by using the brew switch command. This can be useful when certain packages require specific versions of dependencies. Nix, on the other hand, uses a unique approach to version management. It allows users to have multiple versions of packages installed concurrently, each in its own isolated environment, without conflicts. This makes it easy to test and switch between different versions of packages.

4. Reproducibility: Homebrew focuses on providing a convenient and user-friendly package management experience. However, it does not guarantee full reproducibility of package installations across different systems. Nix, on the other hand, is designed with reproducibility in mind. It ensures that package installations are fully declarative and can be reproduced exactly, even across different machines or operating systems. This makes it particularly suitable for environments where reproducibility is critical, such as scientific computing or large-scale deployments.

5. Rollbacks and atomic upgrades: Homebrew does not provide built-in support for rollbacks or atomic upgrades. If a package installation or update fails, it can leave the system in an inconsistent state. Nix, on the other hand, supports atomic upgrades and rollbacks by design. It uses a transactional approach to package installations, ensuring that either the whole set of changes is applied successfully or none of them are. This provides a more robust and reliable package management experience.

6. Customizability and extensibility: Homebrew provides a simple and easy-to-use package management experience out of the box. It focuses on usability and simplicity, which makes it accessible to a wide range of users. Nix, on the other hand, is highly customizable and extensible. It allows users to define their own package sets, package versions, and build configurations using a functional programming language. This gives users a high level of control and flexibility over their package management workflow.

In Summary, Homebrew and Nix are both powerful package managers, but they have key differences in their approach to installation, package availability, version management, reproducibility, rollbacks, and customizability.