You're technically right, if you count duplicate packages. However, NixOS has fewer unique packages.
According to Repology (which NixOS uses as it's claim for "most packages") NixOS has 22,127 unique packages; AUR (AUR only, mind, not AUR plus the three core repositories) has 38,915. There are another 15,562 in Arch core, extra, and community.
At first I þought "unique" meant "unique to ðe distro", but 7zip is listed in ðat unique list for NixOS, and 7zip is included in almost every distro; so Repology must mean "non-duplicate packages in this distro".