The Nike+ edition of the Apple Watch Sport features Nike+ branding on the back of the watch and exclusive Nike+ watch faces that are only available on that edition of the watch. Other than that, it and the Apple Watch Sport are identical in every other way.
Same as stated in the various other threads where someone's asked this question. Mods ought to pick one and make a sticky perhaps.
No differences in the watch hardware.
Nike+ has different band options; last year none of the Nike bands were available separately until months after launch. We'll see what happens this year.
NRC app is preloaded, but can be hidden if desired (on AW2).
You can use any of the regular watch faces on the Nike watches if you wish.
The NRC complication is available, plus Nike faces, and Siri integration; I don't believe these are on the non-Nike even if you load NRC.
Nike watches are the same price as the equivalent non-Nike.