RE: Brake on a Esc ?
Little more to it than that.
The most effective way to slow down an aircraft with respect to the propellor is to have it spinning at a speed slower than the surrounding airstream. The least effective way is to have it completely stopped.
If you use "hard" brake - or on - when you close the throttle the prop will stop spinning entirely. When you use soft brake (or off) the prop will be spun by the motion of the aircraft through the air (like the wind driving a wind mill) - this will produce a much faster reduction in airspeed than if the prop blade was stationary.
For general powered application brake off is probably best, but if for example, you want to have a gliding contest with your power aircraft with your mate, just sneakily turn on your brake before you leave the ground. In glide with no power you will perform substantially better due to the reduced drag.
Cheers,
Oz.