I’ve never used Ansible, but I used Chef before starting to transition to NixOS.
I believe Ansible has a Convergent model of system configuration whereas NixOS tries to achieve and comes much closer to achieving a Congruent model (see Why Order Matters: Turing Equivalence in Automated Systems Administration for definitions of those terms).
An example of this is at a company I worked at, we had a list of users who have access to the systems. When someone leaves, we want to remove them as a user from the systems. On Chef, we have to add a line to our user configuration like remove_user :john_doe. In NixOS, we remove the nix expressions for that user. We could probably write some script that implements declarative users in Chef, but in NixOS this is already well integrated. I believe these differences permeate the ecosystems.