Bicycling

I'm throwing out a guess, but the force required to stop an object is related to the square of velocity. You'd need to integrate force over the stopping distance to know for sure, but with that squared term going downhill it's almost certainly better to apply even force over a longer time. You're going to speed up otherwise, requiring more total force.

For a flat surface, the force is proportional to stopping distance, so the total force is the same regardless of distance, but you need to apply that total force in a smaller time, which for extremely short stoppimg distances surely results in different wear. In that case, it's probably much more complicated and there's some optimal braking distance or optimal braking curve, rather than some simple way to figure it out. I'd say simple advice is that if it's not comfortable for you, that's a good indicator that its causing more wear.

The best thing to do is to anticipate when you'll need to stop, and stop accelarating. Then you'll need far less force to brake. Every day I see people speed up to a light that just turned red, so there's no chance it will be green when they get there. Then they brake and wait 3 minutes. Just let off the gas as soon as you can tell you'll be waiting at the light. Of course be aware of people turning or whatever, but mostly there's no reason to quickly arrive at a light you're sure you'll be sitting at.