There are essentially two schools of riding, especially when it comes to cornering. There is what is often called western, or American type riding, which involves sliding (or backing in) to turns, and there is European riding which is typically smoother. If you watch MotoGP you can see examples of both. Guys like Marquez, Pol Espargaro, Stoner, and Hayden are very good at backing the bike into turns, they do it quite often. Guys like Rossi, Lorenzo and Crutchlow tend to opt for the smoother approach of matching the rear wheel speed and keeping it inline.
When you come into a corner, slam on the brakes, drop a few gears, and let the clutch out, the rear wheel will tend to slow down faster than the bike, which can cause it to brake free and move sideways. The slipper clutch works to reduce this engine braking effect on the rear wheel, and the EBC works with the slipper clutch by providing more RPM from the engine to catch the rear wheel up to actual speed.
I noticed that it was mentioned that EBC is typically in use at maximum lean when you are dropping gears and I want to make sure people know that this is NOT the case AT ALL. You should never have to drop down gears at maximum lean, in the middle of a corner, professionals NEVER do this! You should be in the correct gear for the corner before you start leaning the bike! At maximum lean you should be coming off the brake lever and starting to roll onto the throttle as you come through the apex.
EBC is a matter of choice. If you like backing it in, you won't like EBC very much. If you like things to stay smooth and inline, use the crap out of that EBC and slipper.