Exactly what I was going to say! You beat me to it.Actually, if you look at the formula for kinetic to thermal energy associated with friction braking, it doesn't seem to make a difference since less distance would mean more force and more force would mean more distance. Both would still have the same result:
To add to this, while the braking results would be the same, perhaps the real difference would be the accelerated life of the braking fluid itself. Harder braking = more pressure = more heat = faster breakdown of fluid.
Edit #2: Agreeing with you twice in one day - something must be wrong with me!! lmao