With Nix you have to do everything the Nix way. If a package doesn’t work correctly or is missing you either have to dive deep into the Nix rabbit hole or wait till someone who knows stuff fixes your problem. With nix everything is all or nothing (even more so with NixOS).
Distrobox is the opposite, it embraces variety and gives you as many options/distro environments as it can. Once the missing container bugs are fixed you are dependent on no one to get your packages working.
Also, Nix is usually not the normal way devs package their software, so there always have to be people repackaging the stuff with nix (and updating when the source package changes).
Distrobox gives you access to the environment where the stuff is packaged already, a lot less work is needed to get working packages which should not be underestimated.
The more packages you install with nix the higher the probability you encounter packages no nix expert has cared for recently