I would think it depends on the size and speed requirement.
If high speed is a requirement it's pretty hard to beat an air powered actuator.
Large dampers often have electric actuators.

Small single phase actuators incorporating a capacitor to get the phase shift are quite reliable and can be controlled using simple solid state components. A typical motor would be 230/120 VAC or 24 VAC

I'm trying to think of a 3 phase valve actuator I have seen in modulating service, On/Off is very common. I have only seen reversing starters used to control these although there's no reason it couldn't be a solid state starter or VFD even. The motor would need to match the available 3 phase power.

I'm sure others have different experience.

Personally I have not encountered any 3-phase valve actuators. 3-phase power is much better at supplying high power to the simplest and most reliable motor compared to single phase. However, valve actuators are usually not high power users, and single phase supply is cheaper (less wire). The type of motor used in a single phase actuator can still be of any type, including 3-phase (although it may be called brushless DC). Electronics controls the actuator and the motor. Single phase induction motors using capacitors and/or start switches are cheap but not nearly as robust and reliable as motors without switches and capacitors.

So whether an actuator is powered by one or three phases is ultimately not very important by itself unless you are talking about power levels greater than one horse power continuous requirement. You can achieve the same thing either way.

Thank you all for great answers.

A common easily reversed type of single phase motor has two identical windings, mechanically displaced.
The windings are wire in a wye arrangement, connected together at one end and with a starting capacitor across the free ends of the windings.
One wire goes to the common point and one wire goes to each end of the capacitor.
When either winding is energized directly the other winding is in series with the capacitor and becomes the starting winding.
While this motor could be controlled by a pair of solid state relays, using a pair of interlocked, single pole contactors or switches allows a safety interlock.
While many dual voltage conventional single phase motors may be reversed with only three wires, this is only possible on the higher voltage setting.
Reversing when the lower voltage is used requires four wires.

Bill
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"Why not the best?"
Jimmy Carter