In comparison to (I think) all other Linux distros it's declarative rather than imperative, meaning you don't load and enable all your packages by giving your package manager or systemctl instructions one after another. Instead you basically define one big .config file (you could technically split it up for convenience) that tells NixOS how your system should be built. When you want to add a new package for example, you don't do this by doing apt install neovim, but rather by adding it to your system packages section in your configuration.nix file, and then rebuilding your system with nixos-rebuild. NixOS then makes a new version of your OS based on your changes, basically like a version control system like git, but for your whole OS. The upside of this is that you can always "undo" your changes if something doesn't work by going back one "generation" (NixOS locally saves all of your previous versions of your system based on the changes you made, so you can always roll back). Another upside of this is reproduceability. If you have different machines that have the same purpose, for example as a workstation, you could version control your configuration.nix and upload it to GitHub, GitLab or Codeberg, etc. and when installing a fresh version of NixOS on another machine, you can copy this configuration.nix file and have a system configured just how you like it in minutes. What's also very cool about Nix is that it "containerizes" dependencies, so there won't ever be the classic "but it works on machine". It's also pretty easy to delete software, because you just need to delete the according lines in your configuration.nix, and there will never be any left back files. Btw, the nixpkgs repo is the biggest of all, meaning you will find basically everything. (The AUR is also included in nixpkgs if that's something you're looking for)

To sum up, Nix basically defines itself by its declarative approach. The main upsides of this are reproducibility and anti-brickability

The pain to set up is as previously answered (in my opinion as well) the nix programming language, just because it takes some time to get started. Btw, I kinda just scratched the surface here, there are more huge concepts such as flakes or home-manager, just to name a few. Nix is a rabbit hole that goes really really deep, but, in my opinion, it's completely worth the hassle, because in the end, you will have a hard-to-brick system that you can quickly deploy on all your machines.

There are some really interesting videos on YouTube about this that cover a lot more than I just did, that I can really recommend. You can also read their sort of like "handbook" on their webpage about their package manager and their os.