So, in summary, is a binary Gentoo functionally equivelant to Arch Linux, but with more control over the system?
Perhaps, if that’s how you view the world. I’d argue that it’s better as I’ve never seen Gentoo ship a version of curl that broke Portage…
I would like to know more about the following:
Does the OS installation change, and, if so, how?
You basically unpack a tarball, select a kernel, install a bootloader, and go. It’s no different to before except that you can optionally choose to enable the use of binary packages.
Does package installation, updates, and maintenance change, and, if so, how?
If comparing to arch, you use portage to handle that but the concept is the same.
Gentoo has a great system for managing configuration changes when a package updates a file that you’ve customised.
Do system updates change, and, if so, how?
This question doesn’t make much sense to me. What is a “system update”? Isn’t that just updating all of your packages at once?
Do you lose any potential control over the system when using the binaries, rather than compiling from source, and, if so, what?
Yes and no. If you customise your USE flags the binary won’t be suitable and instead portage will build the package as you requested it
Are there any differences in system stability? Can I expect things to break more readily on a binary Gentoo compared to Arch Linux?
Hahahahaha. Hahahahahaha. Hahaha. Ha.
Arch is notorious for shipping barely tested software to have the higher version number in their repo.
Gentoo enables users to select the stable or testing path, on a per package basis, so you have to opt into packages that haven’t been well tested and even those are typically better tested than arch.