I get the thinking (because it's my first thought too), but the basic force formula (F=M*V^2), means velocity is the greatest influence on Force.

So braking from the higher speed will result in a greater force, meaning more energy dissipation.

I think. Maybe there's something I'm missing here, like including the time to convert that energy to heat via the brakes. Perhaps in the end it's all the same (braking early and keeping speed down), since we're always converting the energy imparted by gravity to heat.