Think I'll chime in here and add my two cents to these other good answers. There are two components to the original question:

1. How much less power does will the 3 phase A/C compressor unit use?
2. Longevity of three-phase motor versus single phase

Power

Motor Efficiency = Power Output / Power Input

It takes a certain amount of power to run the compressor regardless of single or three phase power... this is the power output. The power input is what you are trying to minimize, thus you want to increase efficiency as much as possible. The trouble is this metric (efficiency) is a hidden combination the components inside the compressor unit (compressor, fans). It is not necessarily true (but it usually is true) that three phase is more efficient than single phase.

I would look at the SEER rating which 'automatically' includes the motor efficiency for a better indicator of "cost to cool".

Longevity and Reliability

Three-phase motors and compressors are generally more reliable than their single-phase couterparts. But like anything else, there is more to it than that one attribute. Using Philps' automotive engine example, a 4 cylinder Honda might be more reliable that that old smallblock V8.

Vibration

Certainly less in the three-phase motor. And generally less vibration equals greater reliability.

Motor Starting

Three-phase motors have lots of starting torque and don't (typically) require any special circuitry to start (capacitors, centrifugal switches). And of course fewer components means fewer things to go wrong.

Cost

Is disappointing that the three-phase equipment is more expensive. Almost always, three-phase motors are actually cheaper than an equivalent single-phase motor.

Warm climates are good candidates for heat pumps.

Heat pumps have more efficiency in heating mode when the ambient temperature is warmer, less efficiency when the ambient temperature is colder.

If the outside temp falls too low, the heat pump stops providing useful heat. This is why heat pumps are often supplemented by "emergency" electric heaters that kick in when the outside temp falls too low.

Heat pumps can be more efficient than electric resistance heaters because they only need to move heat energy around, rather than create heat. When the outside temp falls too low, however, it takes more energy to move around the very small amount of available outside heat than it would to just create the heat with an electrical resistance heater.

According to wikipedia:

This typically occurs around −18 °C (0 °F) outdoor temperature for air source heat pumps. Also, as the heat pump takes heat out of the air, some moisture in the outdoor air may condense and possibly freeze on the outdoor heat exchanger. The system must periodically melt this ice. When it is extremely cold outside, it is simpler, and wears the machine less, to heat using an electric-resistance heater rather than to overload an air-source heat pump.