Pixel phones will ship with a new Android version: 7.1. It looks like many of the important Nougat features have been left out from the 7.0 release.
Android 7.1's unofficial changelog published by Android Police has many Pixel-specific features, including a new launcher, a new camera app, Google Assistant, a support tab in the settings, solid navbar icons, Smart Storage that removes old backed up photos and videos when storage is full.
There are also some features that aren't restricted to Pixel devices: night light (filters blue light), fingerprint swipe down gesture, seamless A/B system updates, Daydream VR mode, support for app shortcuts and circular app icons, keyboard image insertion, manual storage manager and more. Unfortunately, Nexus devices and Pixel C will only get a dev preview by the end of 2016, so the stable release will be available in 2017. So much for buying Nexus devices to be the first to get the latest Android updates.
Google Assistant won't be a Pixel exclusive for long, since it's a core Google feature that needs wide adoption. I assume that the launcher and camera app will be also available in the Play Store at some point.