No way a bicycle brakes harder than a car. Weight transfer limits braking force, all the available weight ends up on the front wheel, braking harder does work but is unsustainable because your rear wheel lifts off the ground.
Don't worry about the mass of the vehicle, or the size of the brakes. Both are entirely irrelevant. All other things being equal, a heavier vehicle will have a lower coefficient of friction, increasing stopping distance, but things are very much not equal. It's all down to tyres. Put super soft slicks on a truck and it would outbrake a sports car on a set of old economy tyres.
The size of the brakes only affects two things; 1) the amount of pressure you have to apply in order to generate the same braking force, so with smaller brakes, you just have to push/squeeze harder 2) how long you can brake for before the braking components overheat and become ineffective. This is why racing cars have larger brakes than road cars, despite weighing less. It's not because road car brakes can't stop a car as quickly as the tyres allow, they just can't do it over and over again.
Crashgate3 - stopping from 20mph in 4m requires a little over 1g of braking. I think your estimate is a bit off there. I'd guess it being at least double that.