Do bigger brakes give more stopping power? No. Stopping power is determined by the coefficient of friction of the pads (which doesn't take pad area into consideration).
Do bigger brakes give any performance advantage over smaller brakes? Yes, eg, better heat dissipation. (Heat the number 1 enemy of any brake system)
https://www.cquence.net/blog/big-bra...-do-they-work/
Do bigger brakes give more "modulation"? Not necessarily.
"Modulation" depends on 2 things:
1. the mechanical property of the brake system
2. the human hand, which is a trained behavior
You can give the exact brake system to 2 different riders, and each will invariably describe that the brake system feels different to them. This is because of the human factor; some people like it soft and gentle, some like it hard and abrupt, when it comes to braking. It's some they learn and have mentally adapt their fingers to do. It's a muscle memory thing. But in general, the bigger the disc rotor, the better the modulation will feel to the rider. But of course bigger rotors also have their own issues, like warping, and contamination.