For three phase vs single face, the amount of copper doesn't go up since the current is shared across the additional conductors-- generally the amount of copper required is actually lower due to power factor improvements.
However, for low capacity hops the cost of additional insulation and extra copper needed to achieve ampacity (for worst case fault currents-- the cable must have higher capacity than the breaker so the breaker trips first and with 3ph you have three over-provisioned conductors instead of two) may make it worse off.
However, for low capacity hops the cost of additional insulation and extra copper needed to achieve ampacity (for worst case fault currents-- the cable must have higher capacity than the breaker so the breaker trips first and with 3ph you have three over-provisioned conductors instead of two) may make it worse off.