Guix and Nix are both implementations of the functional package management idea. Nix has been around for quite a few more years than Guix.
In Guix package expressions are first-class and the DSL is embedded in Guile, a general purpose language, so packaging has a very different feel to it. It also allows for fun tools like "guix graph".
Guix is used in scientific environments (e.g. where I work); I don't know if there are deployments of Nix in HPC environments. I do think that there are more bioinformatics tools packaged for Guix.
Another difference is in how the two projects approach certain problems, such as bootstrapping from binaries. (Guix just got a new Java bootstrap from C.)
There is no rivalry between these projects and members of both projects cooperate in the reproducible builds efforts.
If someone came along and offered a hardware-compatibility repo or redistribution, would the Guix community work with them, or would the relationship be more distant, or even adversarial?
I'm personally very interested in the project, and have no desire to poison the pure core of Guix, but I need my hardware to work.
But as a project following the Free System Distribution Guidelines (GNU FSDG) we will not recommend third-party channels providing proprietory software, nor would we want our project's communication channels (mailing list, IRC, etc) to be used to steer users to channels that provide non-free software.