There is a lot of hype about Raspberry Pi Zero recently, but we do not share it fully.
Raspberry Pi Zero is not powerful enough to run APM:Copter at 400Hz reliably. It is just the same as it was with overclocked A+/B+ . You can run Rover or Plane, but you will have almost “Zero” processing power left for any other task, even establishing an SSH connection might be an issue.
Emlid strongly recommends using Raspberry Pi 2B.