...bigger pistons means more displacement, means more pedal travel

...smaller pistons means less displacement, means less pedal travel

This is just one application of braking. Once you start going in/out of the brakes, and in/out of ABS and really pushing the car around on the braking limits, the different kits will behave differently (reaction time, etc.).

Of course, this assumes all else is equal, which it rarely is. Pads will skew this beyond all recognition once you start messing around with different compounds, and different stuff front vs rear.