nix manages the environment too, all direnv is doing in my setup is automatically entering and leaving environments based on my current working directory. Looks like mise does that automatically, which is neat.
mise looks nice, uses PATH manipulation rather than asdf's slow wrappers, and it supports Windows, which is a point over nix. nix only supports unixy environments like Linux, Mac, and WSL.
What might tempt a mise user to try nix are its just truly stupendous collection of packages, so more tools are available. You can also easily add your own packages, either upstream or privately. nix is bigger, more ambitious, more principled, but more complicated. You can build an entire fully-reproducible operating system from a short nix config. It's really cool! But also a lot more to learn, more surface area, more places to get confused or to spend time fiddling with configs rather than solving the actual problem.