Master Cylinder question.

You want the bigger piston for manual brakes.

For example if you can create 700 pounds of force with your leg on a piston with 1 square inch you are creating 700 psi in the system. If you had a larger bore master cylinder that was 2 square inches that same 700 lbs would generate 1400 psi.

The power brake booster amplifies your leg force so you don't need as big a master cylinder bore to get the same pressure in the system.