When you think about the power in kW and compare that to the battery's capacity in kWh it should become a bit more obvious.
Something with 300kW motors will consume more electricity than something with 200kW motors. If the battery is the same capacity, say 100kWh, then if you go full bore flat out you'll drain the battery in 20 minutes in the 300kW car, but you'll drain it in 30 minutes in the 200kW car.
We all know speed = distance/time. So multiply speed by time, and you'll get the distance.
This is all very simplistic, obviously, but in principle that's the physics of how range works.
Its no different to a more powerful ICE car draining a fuel tank faster than a less powerful one.
Also remember, power = torque x rpm x mathematical constant. This applies to EVs too. More powerful motors will have more torque, so they'll produce more power throughout the rev range of the motor, which means even at lower throttle inputs, its still draining more power from the battery than a less powerful motor would at that same throttle input. It would just be accelerating faster.