Yes 3 phase power is cheaper to operate than single phase power.
This is especially true in industrial applications and buildings that use a lot of power such as manufacturing plants, large stores etc.
When a business or factory has a lot of high powered electric motors etc to operate then they will opt for 3 phase power and electric service so they can run more amperage and have it cost a bit less than single phase power.
Homes and small businesses usually use single phase power while large industrial businesses use 3 phase power.
The difference between a single phase and a three phase electric meter and service are that the three phase meters use 3 incoming wires to supply the voltage needed.
Single Phase meters and electrical services use 2 wires to supply the voltage.
Three phase meters and electrical services are used in areas that require a lot of energy, such as industrial areas where large appliances are used.
Single Phase electric service is used for mostly residential places and small businesses that only need a smaller use of electricity.
Single Phase electricity works with 2 wires but three phase electricity service works with only 3 wires.
The other difference between 3 phase and single phase electricity service is the voltage supplied to the meter and meter box.
With single phase electric service there's 240 volts of electricity being supplied to the electric meter and with three phase electric service it's usually 400 volts to 415 volts of electricity being supplied to the electric meter.