The fastest that you can stop any bike of normal wheelbase is to apply the front brake so hard that the rear wheel is just about to lift off the ground. In this situation, the rear wheel cannot contribute to stopping power, since it has no traction. [i.e. this is the extreme case where the weight distribution under emergency braking is 100% on the front wheel; but under more moderate braking there is still more weight on the front wheel than the rear.]
The rear brake is O.K. for situations where traction is poor, or for when your front tire blows, but for stopping on dry pavement, the front brake alone provides the maximum stopping power, both in theory and in practice. If you take the time to learn to use the front brake correctly, you will be a safer cyclist.
Many cyclists shy away from using the front brake, due to fear of flying over the handlebars. This does happen, but mainly to people who have not learned to modulate the front brake.
The cyclist who relies on the rear brake for general stopping can get by until an emergency arises, and, in a panic, he or she grabs the unfamiliar front brake as well as the rear, for extra stopping power. This can cause the classic “over the bars” crash.
Jobst Brandt has a quite plausible theory that the typical “over-the-bars” crash is caused, not so much by braking too hard, but by braking hard without using the rider’s arms to brace against the deceleration: The bike stops, the rider keeps going until the rider’s thighs bump into the handlebars, and the bike, which is no longer supporting the weight of the rider, flips.
This cannot happen when you are using only the rear brake, because as soon as the rear wheel starts to lift, the rear wheel skids, limiting its braking force. Unfortunately, though, it takes twice as long to stop with the rear brake alone as with the front brake alone, so reliance on the rear brake is unsafe for cyclists who ever go fast. It is important to use your arms to brace yourself securely during hard braking, to prevent this. Indeed, good technique involves moving back on your saddle as far as you can comfortably go, to keep the center of gravity as far back as possible. This applies whether you are using the front, rear or both brakes. Using both brakes together can cause “fishtailing.” If the rear wheel skids while braking force is also being applied to the front, the rear of the bike will tend to swing past the front, since the front is applying a greater decelerating force than the rear. Once the rear tire starts to skid, it can move sideways as easily as forward.
…Skilled cyclists use the front brake alone probably 95% of the time, but there are instances when the rear brake is preferred:
Slippery surfaces. On good, dry pavement, unless leaning in a turn, it is impossible to skid the front wheel by braking. On slippery surfaces, however, it is possible. A front wheel skid almost always leads to a fall, so if there is a high risk of skidding, you’re better off controlling your speed with the rear brake.
Bumpy surfaces. On rough surfaces, your wheels may actually bounce up into the air. If there is a chance of this, don’t use the front brake. If you ride into a bump while applying the front brake, the bicycle will have a harder time mounting the bump. If you apply the front brake while the wheel is airborne, it will stop, and coming down on a stopped front wheel is a Very Bad Thing.