I successfully ran OctoPi on a Zero W, using Prusa's image, with a Pi Camera Module. Worked ok, even when printing, streaming video, and doing timelapse, all at once. No issues.
Note this is with a Pi Camera Module, which uses its own interface to the Pi, not a USB webcam. From all I've heard the Zero W can't handle a USB webcam.
However, I did just change to a Pi 3. Why? Mostly because it was very slow on non-printing tasks. Bootup took close to 5 min from power-on to web interface responding. I wanted to add a mesh-leveling plugin that needed to be compiled. That took over 30 minutes of just compile time (and I had to do more work to get it to work at all, since using stock commands led to various timeouts). Things like that.
Now I have a Pi 3. The downside is two more cords to manage. The upside is that it's way faster, and I plan to add a second, USB camera, to have a second POV on the print. I also plan to use the GPIO pins with the Enclosure plugin, and breaking those out with the Zero W inside the einsy case would be more of a pita.