In my understanding, brew will let you only have one version of Rust installed, whereas rustup lets you have multiple.
I treat brew like the system package manager on Linux; that is, if it's a technology I'm actively developing in, I don't use it, and use custom toolchain build stuff. But if I'm not actively developing in it, I use the system manager.
So I would argue brew is correct if you're not actively hacking on Rust stuff, but have some sort of need for Rust on your system, but rustup is correct if you're actively developing Rust code.