nix != NixOS, by the way
Nix is a build tool, package manager and programming language. By itself nix cannot deploy systems like ansible can.
NixOS in turn is a deployment tool similar to ansible that comes with its own distro.
The main reason I’d use NixOS over ansible is that with ansible you can never be certain that the deployment was applied correctly.
Ansible is what we call “convergent”, i.e., we run some scripts that change the deployment on the system to hopefully be what we intend it to become, assuming that the current state is what we think it is. Unfortunately, state drifts, so eventually things can drift apart and start failing. You end up having to take extreme care writing your scripts to avoid causing issues.
Ansible comes from a time when convergent deployment was still very much considered the state of the art. There’s a reason kubernetes has almost completely displaced it in serious organizations, though.
NixOS on the other hand deploys (mostly, assuming sensible config and software that can handle this) your configurations declaratively. Whatever your configuration declares the state should be will be the state. This is unusual, and it can be difficult to adjust to, but incredibly reassuring.
The exception is data, but we have tools to control that as well.
Obviously you’ll get the answer that NixOS is better asking on the NixOS forums, but I don’t really think there’s a competition here. I would never choose ansible over NixOS; Ansible was neat when we didn’t have better options.
As for the learning curve, there definitely is something to that. Unfortunately, there is very little quality tutorial-style documentation for NixOS. You end up having to cobble together an understanding mostly by yourself.
The community is friendly and helpful, though. If you’re determined, I think it’s far from impossible to learn. Just give it a shot with one or two machines in your homelab, no need to transform everything at once 
You’ll run into a lot of papercuts with your first deployment or two, but once you’ve fired every footgun once it’s a pretty smooth experience.