The big advantage of using a package manager like Homebrew is it makes it easier to keep your Python installation up to date. If you download Python from the website, then to update it means you’ll need to go back to the website and download a new copy of Python (or whatever it is that you need to update that could have been installed with Homebrew).
Also, when downloading installers, I find they tend to clutter up my downloads folder and require me to periodically clean up unused files. I’d rather spend my time coding instead of managing my disk space usage.
When it comes to updating any package with Homebrew, the command is simple:
brew upgrade
And this will update all outdated packages that you installed with Brew.
Now, this isn’t something unique to Homebrew. Macports, PIP, npm, Maven, and other package management tools are also able to manage the versions of modules or tools you install.
For more information, see Safari Books Online – Keeping Your Homebrew Up To Date.