Brushless motors aren't faster or more powerful or 'just better' than brushed, you can find a brushed motor that will match the performance of any brushless motor. The big advantage a brushless motor has is considerably less maintenance.
A brushed motor has the motor windings on the armature that rotates in between the magnets, so you need to get power to them to switch between the different coils as it rotates. It does this by a pair of replaceable brushes that ride on the rotating contact segments on the armature.
A brushless motor is built the complete opposite way round, so the magnet is in the middle and rotates inside the windings that are in the can. The advantage is that you don't have to get power to the rotating centre of the motor. The coil switching is done in the brushless ESC.
To keep a brushed motor running at its best you need to keep the commutator the brushes ride on clean and round, usually by regularly skimming it on a motor lathe, and you need to replace the brushes regularly. This means to maintain performance you will need to regularly rebuild and you will have to replace the motor when you wear it out.
Brushless means you don't need any of this maintenance and as long as you don't overheat the motor it will just keep on going as the only parts that can wear are the bearings. Brushless motors are more expensive, but in the long term the manufacturer is only selling you one motor instead of a whole bunch of brushed motors when you replace them after you wear them out.