In normal driving conditions, you will most likely never notice any type of difference. With higher horsepower cars and increased wheelspin, the difference is much more noticeable. The once caveat would be in the snow, where there is increased wheelspin. In those conditions an LSD may be useful as well.
"The main advantage of a limited slip differential is shown by considering the case of a standard (or "open") differential where one wheel has no contact with the ground at all. In such a case, the contacting wheel will remain stationary, and the non-contacting wheel will rotate freely—the torque transmitted will be equal at both wheels, but will not exceed the threshold of torque needed to move the vehicle, and thus the vehicle will remain stationary. In everyday use on typical roads, such a situation is very unlikely, and so a normal differential suffices. For more demanding use, such as driving in mud, off-road, or for high performance vehicles, such a state of affairs is undesirable, and the LSD can be employed to deal with it. By limiting the angular velocity difference between a pair of driven wheels, useful torque can be transmitted as long as there is some traction available on at least one of the wheels."