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.

Rather than focussing on how it's done (inverter drive) focus on what it does (variable speed compressor)

Essentially, the variable speed allows the compressor speed to match the cooling load, so rather than a fixed speed compressor starting, cooling, stopping, starting, cooling, stopping a variable speed model can simply adjust its speed to match the cooling load, while running continuously (until there is no cooling load, or one below the minimum speed it can run efficiently, anyway.)

That has several potential benefits - one is that starting the compressor motor takes considerably more power than running it - so many starts and stops add up - this (alone) might be what someone who says "they only save power over 8 hours or more" is speaking of. However, I think any such statement is far too general to pay much attention to, given the variations in individual units (I've been considering mini-split heat pumps, and have read a lot of data sheets - some are surprisingly different even for closely related models made by the same factory...)

Additional benefits are that rather than the system blowing air that's cold, and then stopping, it blows air that's cool, all the time. Among other things, this improves dehumidification performance and is also usually more comfortable.

You state that you use your air conditioning less than 8 hours per day - but how many days a year? It is true that if the initial cost of something you use rarely is much higher then the payback for any more efficiency (from a unit costing more) is very long (and may exceed the useful life of the product, in some cases.) However, that is not something that is amenable to analysis from afar, and will vary with the initial cost, the energy cost, the use, the climate...

If your cooling needs are limited, and the cost differential is high, just look for the best efficiency among the lower cost type units, and don't worry too much about "the future of HVAC" if having it does not make personal economic sense for you. Something better may be invented before this air conditioner wears out...

Of course, if you are buying 9 of the things, you should at least consider a central system. But that may not pay off in a reasonable time, either.