I don't know how it compares to a Pi Zero, but I had a version 1 RPi and it was definitely not able to run Kegberry. Everything was wicked slow and there were many timeouts. It runs much better on a v2 RPi.
The v2 RPi also has issues; I've taken to adding a cron entry to reboot the thing every night at midnight. That seems to keep it going. I see similar issues with another RPi of mine, so I blame it more than Kegberry.