To say that Nix is a better screw driver is like saying that you could write the same level quality and reliability of software using Bash as in Rust. Rust is just a better screw driver than bash - I suppose it's true in some technical legal sense, but most people won't agree, and it's not true in any sense that is useful or valuable.
They're declarative, idempotent, and intended to manage infrastructure, operating systems and clusters, and coordinate application delivery, key rotation and configuration. Repeatability, rollback, and version control are the basic design tenets.
Sorry to hear that an OS upgrade broke your scripts once, but that's hardly the fault of configuration management tools in general or the Puppet/Ansible/Chef/Salt family in particular.
As you might tell from between the lines, I have some experience with these tools in various environments. But I also see the need for another generation, mainly because of the large shift to Kubernetes application delivery. The insistence of these tools to manage the entire OS stack makes people regard them as too complex for what they need. It is my personal belief that the concept of a host is limiting the continued acceptance of this type of tools and I have been spare time experimenting with other primitives to describe state on, such as binary file archives.
Playing with Nix, it is my impression that it is quite similar to other configuration management tools, a host is still the basic entity we serialize state on. State transitions are a linear graph.
What people describe as problematic with configuration management in general is usually perceived complexity, and Nix seems to have the potential for more of that. But I have not used Nix in anger, or in any type of real world complex environment, and I would be very happy to learn from someone who has experience.
That's what I'm saying, they are not declarative or idempotent in my experience, at least not Ansible. I'm not as familiar with Puppet so I wont say anything too confidently with that, but Ansible is 1. not idempotent as it allows you with ease to execute operations that can modify the system differently based on the system's state, and 2. not declarative, as the operations are step-wise.
Anyway sounds like you have experience and an interest in the field. My experience with Nix is more personal than professional but I'm happy to try to answer any questions you have about it.
Each and every point listed here could have be taken verbatim from a ten year old blog post why Puppet, or later Ansible, is the new great thing. Being declarative and idempotent is the basic design idea of these tools.
Managing every layer of infrastructure and the entire OS stack is also exactly what they aim for, and ironically also what many people regularly quote as why they haven't taken off more. Git support, and module versioning, is also completely on point. What is it that Nix does differently, and why? Is it a fundamentally different type of tool, such as Puppet is from plain Ruby scripts, or is it a better screwdriver?
That Nix is a distribution in itself is an important difference. But how does that affect the use case?
I realize the question have been asked before, but that's because not many attempts are ever made to explain where it sits in the problem space. It is not written for anyone who has experience with configuration management and infrastructure as code tooling, but instead for passive observers with the intention of bootstrapping the next hype cycle?