Is the "efficiency" of car brake affected by how much force is applied by the brake?

Is the rate which the break wears out dependent on how heavy you step on break (assuming car weight, road condition, etc are constant)?

Yes, it matters. If you press the brake lightly, then a small pressure will be created in the brake piston, and the braking force will be less. So, the brake shoes will wear out less.

On the other hand, if you brake firmly, then more pressure will be applied on the brake shoes, which will increase the braking force and thereby, increase the wear.

Someone argues with me that stepping on car break for long periods of time will wear out the break faster than applying break for short periods of time.

If I consider that you apply same pressure on brake pedal, then it depends on the total time of braking. For example, if you brake for shorter periods of time, but the total time of braking is exactly equal to the time you press the brake in case of a long brake, then the wear will be equal.

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Braking wear actually depends on two factors together:

Time of braking - greater the time of braking, greater will be the wear of your brake shoes

Pressure on brake pedal - greater the pressure, greater will be the wear and tear.

Important disclaimer: Don't take driving advice from one random person on the Internet, this answer is provided for the purpose of answering this question and not for teaching how to drive. Always apply brakes sufficiently for distance vs. time to stop vehicle rather than concern yourself with breaking your brakes. This site and the author accept no liability for results or injury from posts on this website.

This answer assumes identical conditions in all cases including type of brakes, the materials that the brakes are made from, correct bedding, and identical "non-brake components" including but not limited to brake fluid, hoses, tire pressure, etc.

There are basically two parameters, duration and pressure; it is a complex combination of the two which factors into braking within the required distance. In practice there is much more than those two factors to consider.

First, "not using brakes" tip is: if the light is yellow, it is safe to proceed, and you are near the intersection then apply acceleration. If you are far from the intersection take your foot off of the gas and allow the engine and friction to replace brake usage. Never apply acceleration late on a yellow far from the intersection, forcing harder usage of the brakes, to avoid running the red.

The reason the prior paragraph is relevant is because heating your brakes increases the wear in addition to the usage - cold brakes wear less than hot brakes, so keeping them cool is a factor in addition to duration and pressure.

There are two primary mechanisms of friction at work during the stop: 1) adherent friction and 2) abrasive friction. For adherent friction, a thin layer of material is continuously transferred between the brake pad and the rotor. The breaking of the chemical bonds creates a resistant force to stop the vehicle. Abrasive friction is the mechanical wearing of the rotor and friction surface, like sand paper on wood. Brake pads use both mechanisms, but at higher temperature, adherent friction is what stops the car. The brake pad deposits material on the rotor, and as the pad gets hot, more material gets deposited. Source: https://www.powerstop.com/what-causes-brake-pulsation/ .

Also see: Abrasive Friction Vs Adherent Friction — PureForge® Rotors - Part 1 (Abrasive Friction) and Part 2 (Adherent Friction).

High pressure for a short period of time increases heating and pressure upon the components (including piston seals). [Remember disclaimer: If you feel you must jam on the brakes to avoid hitting something that is preferable to being concerned with breaking your brakes.]

Low pressure for a longer period of time reduces wear (in part because friction from non-brake sources, road and engine, reduces the wear).

Jumping on the brakes, rolling forward and jumping on them again, (along with increased wear on the suspension, possible wheel locking (which you specifically excluded from consideration in your question) and an uncomfortable ride) causes increased heating and rips off the face of the braking surface (as opposed to simply wearing it down).

In any event, last second jamming on of the brakes is better than not stopping when needed - but you should always plan to avoid that regardless of being cheap about wearing out your brakes.

So: look, anticipate, plan, use non-brake friction, and apply early and gently two or three times (if necessary) to keep the pressure low and reduce heat; along with avoiding shearing the surface, wearing suspension, jerking the vehicle, wearing the seals, pressurizing the hoses, bending the components.

There's more than the pads or drums to wear out and braking isn't strictly pressure and duration involved in wear upon the whole system.

In general, the stronger the brakes are applied the sooner they will wear out - all other things being equal.

But perhaps your friend is confusing the effect of "brake fade" - counter intuitively, when brake fade is a risk, the brakes should be applied immediately at the fullest force to bring the vehicle under appropriate control, otherwise their effect will wear out (perhaps irrecoverably).

If the brakes are feathered for long periods (as on a downhill stretch, for example), they will fade to the point that wear is rampant but friction (even under a full application) is minimal.

And in general, a series of sharp applications will cause less peaking of fade (but not less wear) than a constant steady application, because when the brakes are released, air is better able to flow over the friction surfaces and the intense heat at the friction surfaces is given time to dissipate (thereby ameliorating fade and restoring friction).