Guix is a package manager and a GNU/Linux distribution, whereas Chef and Puppet are configuration management systems that work with a number of different distros.
So, rather than using Puppet + Debian or something, you would probably just use Guix, because Guix has system configuration tools[0]. Guix (Nix, too) solves system management problems from the bottom, at the systems level. Other tools tack it on top of existing operating systems.
Guix seems to be a package manager. Chef/Puppet are configuration management tools. In short (from what I understand, I have only read about guix), you can use all of them to install software. But Chef/Puppet give you much more - distribution of configuration data, runtime search between machines, control over services / resources, etc. In practice you'd probably want to use one of them to install guix and run guix commands locally when setting up the hosts.
I don't think guix does system configuration at all. And I don't mean "what software needs to be installed" configuration. I mean, configuration system that says "this is a staging environment, this app logs at DEBUG level via syslog, syslog gets configured to ship errors/exceptions to XXX, app uses local cache not cluster, credentials get pulled and decrypted from ABC".
This kind of configuration goes one level above package management, whether it's guix, apt, yum, pacman, or anything else.
Edit: you actually said benefits of guix in the original question - it gives you the way to make a localised installation of something you want. Chef/Puppet cannot be it on their own.
What Guix and Nix offer over puppet et al is a greater reliability in reproducing an environment - by eliminating the side effects that could lead to errors, or possible configurations and package combinations which have not been tested.
The fun part is that configurations can be treated exactly like packages and vice-versa. A "package" can depend on a specific configuration too. After you realize that package management and configuration management are not really disjoint ideas, it's the only sane way to think about reproducing software reliably.
So, rather than using Puppet + Debian or something, you would probably just use Guix, because Guix has system configuration tools[0]. Guix (Nix, too) solves system management problems from the bottom, at the systems level. Other tools tack it on top of existing operating systems.
[0] https://www.gnu.org/software/guix/manual/guix.html#System-Co...