It has many of the strengths of Portage, and even go beyond (it builds from source, and users may configure package dependencies, like USE flags on steroids -- its declarative language used to write packages is also used to configure them, so you can do more than just passing flags to a package). But it offers a substantial advantage, because builds are deterministic. The set of installed software (with all needed configuration) is determined from a config file (or many), and from this it's always possible build the same system.
This means that upgrading always end up in the same state as installing from scratch. This also mean that common packages can be cached as binaries, without risk of breakage - it only downloads a binary package when building from source would build exactly the same binary.
Nix also feature atomic upgrades and rollbacks: it only touches the running environment as the very last step of the upgrade (setting up a symlink), and stores the previous versions of packages until garbage collected, so an upgrade stopped in the middle can't break your system (the exception here being kernel upgrades). Indeed, if you interrupt an upgrade or install at any stage, just issue the command again. (also, this architecture makes it incredibly concurrent)
NixOS is a distro that uses Nix. It can provide a GRUB menu to boot previous versions of the system. When you upgrade, you can have it affect running system or only upgrade after a reboot. Either way, when you reboot GRUB will give the option to also boot the system you was using before the upgrade. On a technical level, Nix works a bit like a git repository: each package is addressed by the hash of its derivation (that says how to build it, and all its dependencies), and if more than one system version uses the same package it gets stored only once.
Coupling NixOS with Nixops, a deployment tool; and Disnix, that does service-oriented deployments (like Docker), they can help build more repeatable systems for production servers too.
Some links: