In riding, one of the most confusing questions is which hand should control which brake? In the United States, all bicycles must be sold with the left hand controlling the front brake and the right hand controlling the rear brake. This is also the case in France. Interestingly, this is not the case in Italy or the United Kingdom.
Classic bikes with exposed brake lines make it easy to see which lever is connected to which brake. Modern bikes hide their cables under the handlebar tape.
Historical Reasons for the Arrangement of Brakes Left and Right
History is the most likely explanation for these differences: early bikes had only a rear brake. Rim brakes were common in France. Early brakes were not very powerful, so stopping the bike required a lot of hand strength. Since most people are right-handed, controlling the single brake with the right hand made sense. Therefore, the rear brake lever was located on the right. The single brake was a coaster brake in Italy and Britain, and there was no brake lever at all.
At some point during the 20th century, front brakes were added to bikes. This required adding a brake lever to the handlebars. The right side had already been taken in France, so they mounted the extra lever on the left.
Since Schwinn was the only company importing performance bikes with hand brakes, and Schwinn was influenced by French bicycles, the U.S. copied French practice.
The brake lever for the front brake used to be placed on the right side of the handlebars in "coaster-brake countries" (Britain, Italy, Germany, etc.). When racers started using rim brakes on both wheels, the rear brake lever was placed on the left.
If you look carefully at the Baines Flying Gate, you can see that British sidepull brakes have the cable entering on the left side (from the rider's perspective). Therefore, the brake cable coming from the right lever will have a larger radius.
There are historical reasons why some people use "right-front" and others "left-front," but this doesn't answer the question: Which is better?
Which Sort Order is Better?
The "right hand - front brake" approach has been defended for many reasons. Most motorcycles are designed this way, since the right hand operates the throttle and the left hand operates the clutch (via a hand lever), which means that the only place to put the brake lever is on the right side of the handlebars.
Cyclocross racers prefer the "right - front" setup, so they can brake with their left hand as they dismount. Getting your bike to fishtail when you only have one hand on the handlebars does not make sense to me. By the time you release the bars and prepare to shoulder the bike, you should have finished braking. (European cyclocross professionals generally follow their country's practice, with Belgian and French racers choosing the "left - front" setup.)
Others point out that most riders are right-handed, and the front brake is the most useful one, so using your stronger hand to operate it makes perfect sense. A good brake shouldn't require a lot of hand strength...
Can you explain the advantages of setting up your brakes "left - front"? In the U.S., where we ride on the right side of the road, you can stop and hold onto a railing or post with your right hand while using your left hand to operate the brakes. I often use my right hand to shift, eat, or take photos, so it's nice to be able to use the more important brake with my free hand.
Although there are pros and cons for each setup, none are so great that they make one better than the other. Ultimately, it comes down to personal preference.
For bikes with centerpull or cantilever brakes, the brake cables can easily be switched from side to side.
Although most sidepull brakes are set up for "left hand - front brake," even those made by Italian companies like Campagnolo and Gipiemme, most Italian racers route the cables in the opposite direction (below). The front brake cable bend is a little tight (especially with aero brake levers), but it isn't an issue.
For disc brakes, the rotor is on the left, so it works the same way for sidepull brakes: If you use the right lever to operate the front brake, then the cable run has a larger radius, which is especially useful for mechanical discs.
Regardless of what you do, I recommend being consistent. Your instincts will take over during a panic stop, and if you are used to pulling on one lever, if the brakes are reversed, you may find that you are skidding the rear wheel without slowing down much. Many of my friends utilize the "right-front" approach, and when I ride their bikes, I have to constantly remind myself of the reversed brake levers - and hope that I won't have to stop in a hurry.