Apart from coasting as much as possible rather than using brakes, the lighter you apply the brakes, the better, even if it means longer application time
Say your car weighs 1000 kg and you’re traveling 20 m/s. Your car has 0.5* 10002020 = 200 kJ of kinetic energy. If you’re going to slow down to a stop, you have to eliminate that energy somehow. If, for a second, we assume you don’t lock your brakes and they make NO noise, all of that energy is going into heat in the brake pads and rotors. So now matter how you brake, you’ll end up with the same net amount of heat.
However, if you brake more slowly, your heat FLOW is slower, and while that is occuring, you do have convective, conductive, and radiative cooling of the brake parts. And this is crucial.
I’m going to grossly simplify things here, but all of those cooling methods are generally dependent upon the difference in temperature between the parts - so the difference in temperature between the brake rotor and the surrounding environment (again, simplifying things). They’re all roughly (again, simplifying, but a safe one) directly proportional to this difference, too.
So if you look at the system, you have a heat flow in, a heat flow out, and the difference must be accumulated heat energy (thus a temp increase) in the parts. Let’s again simplify things and say we brake until we reach a steady state temperature. So say you brake for 10 seconds or 5 seconds to bring your vehicle to a stop. Let’s pretend (making the number up), that the heat is dissipated entirely by convection, and the convection coefficient times the surface area of the rotor is equal to 1000 W/K
You then have :
Braking energy in = Heat energy out (at steady state)
So in the 10s case, using 293K as an ambient temp:
200000J/10s = 1000 J/s/K*(rotor temp - 293 K )
rotor temp = 313 K
In the 5s case, you get:
200000J/5s = 1000 J/s/K * (rotor temp - 293 K)
rotor temp = 333 K
Even if you don’t reach steady state heat transfer, you’re still going to reach higher temperatures if you brake harder…
And as in the cases of so many things automotive, temperature is your enemy. Therefore, since braking slower results in lower brake temperatures, you will end up with longer brake life.
Even better yet is to not even use your brakes when possible (ie, coasting) - you get ZERO heat buildup then.