I personally like Nix's syntax better than a lisp, but that is just a preference.
The core of how they operate is the same. Just look at their build/ci system.
It's also much more than a matter of syntax: see the great explanation at https://news.ycombinator.com/item?id=18910683 .
That rewrite is bring new features, differences, and makes them not compatible with each other. However, as they started off with the same code to me they will always be a fork. While something can evolve to something that is fully independent, it doesn't change it's origin. Also a fork is not bad word. Many successful "forks" become more popular than the original.
To this day guix still uses the nix-daemon code, which is written in C. And they build system they used was hydra, written in perl. In fact http://hydra.gnu.org used to say "download nix package". for everything. Cuirass is very recent, but you can still see that it still looks extremely similar to Nix's hydra.
I think guix still has better porcelain (cli).
Nix has much better discoverability and readability. I was going to show different files, however gnu.org NS servers seem to be down.
Most importantly it isn't a competition. These two products existing only benefit each other as new ideas between them flow both ways.
Also, nix/guix are somewhat lower-overhead ways to build a system for local development than containers.
This is a good starting point:
So Guix gives you reproducibility, provenance tracking, and hackability, but you can still "speak Docker".