For a detailed "Guix vs. Nix" comparison, see: https://news.ycombinator.com/item?id=16490027 and https://news.ycombinator.com/item?id=23529932.
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!