Assuming you can go either way, is it better to install a Multi-split or multiple Split Air Conditioners?
There are three issues here, which system is better, which system is more energy-efficient and which system is more reliable.

The first issue encompasses all aspects and involves a priority ranking which only you can do.

An issue not brought up by anyone else is the installation. Do you have room for 3 outside units? Does it matter if more space is used or would you prefer to use that space for landscaping or something else?

What about electrical power? Will the installer need to run 3 circuits, one for each compressor? Does your existing breaker panel have the room for 3 circuits?

Another installation consideration: which system is easier to run the linesets (tubes which carry the liquid and gas freon) for?

I expect 3 compressors to cost more than one big compressor. Have you gotten any price quotes?

The one big compressor, assuming it is capable of variable speed, will certainly be more significantly more efficient under anything less than full load because the condenser of a single outdoor unit system has three times the cooling area of a single condenser in a 3 unit system which means the compressor motor doesn't have to work as hard.

The major factor in power consumption is turning the freon back into a liquid and that depends on how fast/easily the condenser can cool it off. All else being equal, a bigger condenser is better (removes the heat faster).

The faster you condense the freon, the less back pressure on the compressor and the less work for the motor.

Most of the time you will not be running full load or all indoor units at once. Even during full load, the big unit will never be less efficient.

The last question is reliability and available. One answer correctly claims that a 3 unit system will be more available but neglects to mention that it will also be more prone to failure because you have more units to fail and each unit is more likely to be run at full capacity while the big unit will usually be running well below its full capacity. Imagine the lifetime of two cars, one run at 90 MPH and one run at 30 MPH.