Motors do not require power. They draw as much power (energy/time) from the batteries as the loads pressed upon them mandate.
Brushless motors are capable of delivering much more power than brushed motors of similar sizes as their efficiency is much higher & they are electrically & mechanically more robust to handle those huge power levels.
They are basically Permanent Magnet Synchronous Motors (PMSM). When 3 phase AC supply is given, then they are called PMAC motors & when 3 phase switched square-wave DC supply is given, then they are called BLDC motors.
For mobile applications like RC vehicles, we have to use them as BLDC as AC power cannot be stored. DC power can be stored in batteries. To convert simple zero frequency DC supply to 3 phase variable frequency one, we have to use a work of 'engineering art' called Electronic Speed Controller (ESC).
But remember that to work as BLDC or PMAC, we require some kind of feedback of rotor position to keep rotor in sync with the supply. In case of BLDC, Hall effect sensors or back EMF sensorless technique is used. In case of PMAC, apart from the feedback techniques used for BLDC, optical sensors are also used.
In short, actually, what we are using in our brushless cars is very futuristic & is the future of our automobile industry! (only if battery tech can evolve...
) Thank God that we live in these times