Reexec is when nixos-rebuild builds the new version of nixos-rebuild from your configuration and reexecs that version so that the bulk of the nixos-rebuild operation is done with the new version instead of the currently-installed version.
It basically just skips that step and only uses the currently-installed nixos-rebuild. Apparently this has been renamed --no-reexec on unstable, which is documented in the nixos-rebuild help / manpage.
Unstable just has a newer version of nixos-rebuild that does things differently. It detects whether reexec will work at all and automatically skips it if it won’t.
Cross compiling. If you configure the system to be cross compiled, you can just nixos-rebuild --target-host root@host to cross compile the system and deploy it, rather than needing binfmt to build it with emulation. Like I said, on stable you’ll need to pass --fast to avoid nixos-rebuild reexec’ing into the non-native nixos-rebuild, and on unstable it figure that out automatically.