Do conductors have high or low current?

Low resistance.

Think of Ohm's law. Voltage drop is directly proportional to resistance. The higher the resistance, the higher the voltage drop, and the less voltage that is available for the load. Think of conductor resistance as a resistance in series with the load.

Also, higher conductor resistance means more power lost, going to heating the conductors. The "line loss" formula is P=I2R. The greater the resistance, the greater the electrical power being converted into thermal power heating the conductors.