Brushless Motor = The new technology, higher efficiency, usually Longer motor Life, but a complex electronic controller with at least three multi-directional current hot wires to the motor from the controller is required.
Brushed Motor = The old technology, lower efficiency, usually shorter motor life, requires brush replacement on a routine maintenance schedule, but a complex electronic controller is not required and if you wanted to you could go as simple as a simple toggle switch with one hot wire from the battery to the switch and then to the motor and a single ground wire from the motor to the battery.
Long story short the brushes in a brushed motor are a mechanical equivalent to the complex electronics in a controller just not near as efficient and subject to wear. There are still a few of the older style brushed hub motors out there if you look hard enough and if you are building your own mid-drive system from scratch there are plenty of low voltage DC motors out there to choose from but you will take at least a 25% hit on the power and/or range you will get out of the same battery pack and if you compare a really efficient top of the line brushless motor to a really inefficient brushed motor it can be as much as a 50% hit.
I do personally believe that there is still a limited niche market for a brushed hub motor. Specifically a low wattage, freewheeling, internal gear reduction, rear brushed hub motor that had a slow speed output that was geared down low with lots of torque specifically for helping a rider who normally pedaled without motor assistance climb hills. Something that pulled between 200 and 500 watts depending on input voltage, that being anything from about 18 to 36 volts that would run off of just a simple toggle switch and a water bottle sized battery pack. Something that would give you a bike that was just a pedal bike most of the time because the motor was geared so low that you could go faster on the flat with just casual pedaling then the motor would push you but when you came to a big steep nasty hill you could just flip a switch and have the motor kick in and help you up the hill for five or ten minutes and then when you got to the top just switch it off again. Something small and simple that was just made for climbing hills and geared down accordingly. It is amazing how strong and how well a little 250 watt motor can climb a steep hill if it is geared down enough.
Another thing I wish someone would make is a throttle control for bikes that plugged into the brushless motor controllers that the remote control guys use for their cars and airplanes. The brushless motor controllers they are using are like a third the price and a third the size and weight of the bike controllers and a lot of them are rated to take huge amperage loads, and yes provided the number of poles matches (usually 4-pole with 3-motor wires) they will work on the same motors we use. I've tried it, just that I don't want to have to hold RC controller in my hand to have throttle control. How the RC controllers work is that they have a small variable resistor in the little stick or trigger on the hand controller and the computer in the controller converts that to a standardized 8-bit binary code for the throttle position and transmits that over the designated radio frequency and the receiver in their little car or airplane reads that code and sends it via a standardized analog feed-back loop arrangement to the brush-less motor controller (a standardization originally intended for servos) and the motor controller responds to this "standardized servo language" tricking the receiver into thinking it is a servo and adjusting the motor speed accordingly. All of the RC brushless motor controllers for years and years have had directionally specific, no hall sensor required, start from dead stop capability that only the very best bike controllers have even begun to be capable of, and most of the better RC car controllers have both reverse, interference braking, and regenerative braking capabilities.
Long story short, imagine a controller that already exists for another industry that average a third the cost, a third the size, a third the weight, can take more amps (a 50A rating is considered where the high load controllers start and anything less is merely standard load in those guys world), completely make hall sensors irrelevant and can start from a dead stop without one in whichever direction (forward or reverse) is desired on command, and in the better higher priced models have not only regenerative braking but programmable interference braking capability as well (basically strong braking action through the motor that does not charge the battery since with some kinds of batteries in some situations regenerative braking can hurt the battery) such that the full power of the motor can be used for braking without hurting the battery, motor, or controller even if you were to go down the back-side of a mountain pass using only the motor to do your braking all the way down. Add to that the capability of having a low speed motorized reverse option on a direct drive hub-motor if you wanted it.
What is needed is a simple and reliable throttle assembly for our bikes that one end mounts to the handlebars and the other end has an RC servo plug that talks directly to an RC type brushless motor controller in the universal electronic RC servo language so we can use their controllers to run our motors. I'm sure though that the current bike controller manufactures really, really, really don't want to see that happen.