Brightness will come from three sources in a mod like this
1) It boosts voltage.
2) It increases the voltage high time of any kind of PWM based brightness control (be it by making it constant voltage or something controlling it).
3) It decreases any current limiting effects (it is common enough to have a LED in line with a resistor to limit the current over what providing it as much as the LED can handle for various reasons).
In classic schoolboy terms then Power = Current x Voltage or P=IV. Increasing either I or V then increases P, at least until something burns out and goes open circuit.
You would also want to know why it works in the case of the replacement -- in the base state is it more "that'll do" was used as a power source for the backlight and with a simple tweak it is improved, can the replacement handle the greater duty cycle or power dissipation in a manner acceptable for your purposes? The worst case is it burns out instantly or near enough as makes little difference (most people would be upset if lifetimes dropped to 2 months, only real exceptions I can imagine being "I need it for a show"). It could also be that it is designed to work in environmental extremes -- you live in a house in the arctic circle and are all "just keep the toilets from freezing up and mould off the walls" in terms of heating and that is radically different to grandma house hot in the tropics.
Even if the brightness boosts and you are happy with any reduced lifetimes as a result (maybe in 5 years the replacements will be cheaper and better still and any battery life reductions don't matter -- most people play within a few metres of a wall socket anyway) there is also the concern about any colour replication -- overdriving a LED can result in colour changes to output. Probably not going to be too drastic here and it is not like the GBA ever had amazing colours/we are doing printer grade work here (if you base your homebrew on output and find it does not look nice on stock devices then... yeah) but something to note in this.
Those are the sorts of questions I ask in such scenarios (though usually less backlight and more general light) and would want answered reasonably well. However I doubt anybody outside of maybe the screen makers themselves (and even then probably not) has any real data on this. Would not be the hardest to do (feed a screen externally or chop it and adjust voltage/pwm/current limits internally with variable whatever whilst sticking a FLIR/temperature sensor on the backlight to get an idea) but also not a 5 minute largely safe project.
