Bigger brakes won't really shorten stopping distances but good tires will. What a big break system does well is make the 50th stop feel like the first and you noticed this by the fact that pads last longer due to less thermal stress.
That is not quite entirely accurate. BBK have opposed pistons, meaning the rotor is squeezed equally from both sides. Possibly larger thermal path, but the rotors are supposed to dissipate the heat, not the calipers.
The two biggest factors BBK's add are:
much improved modulation/feel
almost no pad taper
Thus extending the life of both the pads and the rotors by a HUGE margin. Ultimate stopping performance is related to max deceleration without lock up, so better control = better stopping. I agree that sticky tires make a bigger difference, and will also overtax brakes already at their limit quite easily.
My 3500 lb 444 rwhp street Fox vert had f/r Cobra brakes that I tried various pads with. HPS, EBC Red, EBC Blue. Then added ducting. Shaved 255/20/17 NT01s all around, so that was a lot of grip for a street tire. No real serious fade, but needed more and more pedal pressure to maintain consistent deceleration performance and one hard track day would finish off a full set of rotors and pads. Make sure you have the anti moan brackets installed on the rear caliper brackets to triangulate them for minimizing pad taper and improving rear brake torque.
The two tracks I run at are murderous on brakes, that's why most of the newer cars don't like them because their even heavier mass makes it worse.
Switched the fronts over to Brembo 4 piston calipers, and added dedicated one pc Stoptech slotted rotors and DTC60 Hawk pads all around for the track.
The car entered another zone. Truly remarkable how much faster and confidence inspiring it became. The brake swap between street and track is a PITA, but hard race type pads not only dust badly but wear the rotors out at something like a 10:1 rate vs when hot.
My new setup has 5 hard track days (40-60 laps per day) and the brakes are virtually new in dimensions. I should have installed 17mm thick pads, as they further improve the heat insulation between the rotor surface and fluid, along with stainless pistons; both of which are on my to do list.
I am also going to 18x10 lightweight wheels with Hoosier/Conti 275/35 full race slicks this year, so I will likely need even more pad.
Won't really know anything until the first shakedown; car received MM k member, 1.5" wheelbase extension, 1" engine setback, MM Torque arm and re installed power steering this winter. Car should be 2 or 3 sec per lap faster at min, and a whole bunch easier to drive, now that I don't have to wrestle with the 12" Momo steering wheel unassisted, lol
Some vid footage: https://www.youtube.com/watch?v=3_2yTyzbCCQ
Using slotted and drilled one pc street rotors along with HP+ pads, a little noisy and dusty but can handle hard driving with no fade on the street; likely could take a day at a fast, non braking track.