When I use ffmpeg using nix-shell -p ffmpeg I get a version from the NixOS cache, however if I create a service that depends on ffmpeg (using pkgs.ffmpeg) it needs to build a whole lot of dependencies from scratch, which is painfully slow on a Atom based NAS.
One possibility is that you are pulling from two different channels, once for the user and one for the system. Do you get outputs for both of these commands?