I understand the principle and workings of a "normal" (brush) motor, but have no inkling of the pros and cons of any other type.
The main advantage of brushless motors is that they are much more efficient than brushed motors. Instead of a mechanical connection from the power source to the electromagnets the current on a brushless motor is switched using some clever electronics. The clever bits are in the speed controller hence they used to be much more expensive but that is not the case any more, you can buy brushless controllers for less than the cost of a brushed esc.
A brushless motor normally runs much cooler and is much smaller than a brushed motor for a given power output. In my earlier posting I mentioned that I fitted a brushless motor to my old SHG Shadow, the motor is physically about the same size a 380 motor but is capable of about 350 watts which is far more than a 540 motor would produce.
I have quite a lot of experience with brushless motors in aircraft but I've only just returned to boats. I'm working on my second boat now and that also has a (bigger) brushless motor. In aeroplanes power and weight are critical and using heavy old brushed motors power was marginal but brushless motors together with LiPo batteries have revolutionised electric flight. I'm now using some of my knowledge learned in aircraft on my boats. It's good fun.
Sorry I've rambled on a bit but I hope this helps.
Phil.