I don't understand why a higher power factor would be less current draw. Isn't just the angle between voltage and current different?
Voltage stays the same.
If you are familiar with power factor triangle the base represents true power(watts), the hypotenuse represents VA (which contains the amps that you will measure with a ammeter and what does create heating effects in the conductor) and includes any reactive current -which is what causes us to have a power factor in the first place.
Divide each number by voltage to get current relative to the figure represented. The hypotenuse is always the long side of the triangle and always is the side that also contains any reactive current.
If there is no reactive current the PF is 100%, the watts and VA will both be the same so the PF triangle with 100% PF present is not a triangle but rather just a straight line.