Now however, I decided to expand this project a bit. Took a regular PI3, GPIO expansion board and latched the PiStep2 Quad on the last row of pins. Nothing attached to the other rows of pins yet. On this PI, I've updated everything to lastest version and code is exactly the same as it was on PiZero.
My motors weren't running that smoothly anymore (sometimes one or two motors not running while all 4 should), so I wondered if it could be a power issue... Took 9v battery and changed position of the jumper on Pi, so the hat would take its power from the battery now. Sometimes few of the motors still "slack".