In a nutshell, these are two different projects, with common foundations, but also different technology and different focuses--just like Julia and Clang are different, even though they both use LLVM.
The project blogs and documentation should already give a feel of how those differences play in practice!
It's not just Nix lang it replaces, we use Scheme in place of a hodgepodge of languages (shell script, Nix, C and others). Almost all equivalents to C-hardcoded parts of Nix is inspectable and modifiable in Guix. There's code reuse across the stack. Even the systemd substitute is opened up for inspection and modification. Nix glues a lot of black boxes; Guix is a single white box. Both approaches are practical for different reasons.
The first one primarily just says "we use Scheme instead of Nix lang".
There are some differences that emerge from that, but most of what is described is also common or possible with Nix.
The analogy of clang vs Julia does not fit for me.
Nothing I've seen has yet described any significant difference, but rather affirmed that both are very similar in most regards.