I'm hoping at some point they give the Google Assistant on the Pixel the same functionality as Home.
For example, once you connect Home to your network and setup your smarthome devices with it, you can use the Assistant on the Pixel to control your devices... since your Google account is shared between you're Pixel and your Home, commands can be passed through your Google account to the home to control the devices.
This way your phone can act as mini Home devices to control things in your home.
EDIT: this actually does work... I can control my Hue lights from my Pixel from anywhere. So as I'm getting close to my house I can say to my Pixel, "Ok Google, turn on outside lights".
This didn't work at first for me because I have a generic family account on the Home and my account for the Assistant on my Pixel.