3 phase since it would more than likely be servo.
A single phase machine can be servo drive and AC heads. The servo amplifier and individual frequency drives for each head can take an input of single phase and output three phase to the motors. We have converted three phase machines to single phase and single phase to 3 phase machines.
The three phase machine however will draw much less amperage, which would be a lower operating cost and lower gauge wiring & disconnects/breakers running to the machine. But if you don't have 3 phase, it could be less that having your utility company run 3 phase to your building, depending location.