With a stock setup, when the spring flexes upwards the movement of the shackle forces the axle to shift forward and pushes the tires into the obstacle. The standard shackle setup aggressively attacks an obstacle. Can provide a jolting ride, depending on the springs and shocks.
With a shackle reversal, when the spring flexes upwards the movement of the rear mounted shackle forces the axle to shift to the rear and causes the tires to roll up and over the obstacle. It essentially provides for a smoother transition over obstacles because the suspension gives into the obstacle, instead of aggressively attacking it. Can make stiffer springs ride softer by letting the axle absorb some of the motion of going over an obstacle.
Some say that shackle reversals can make climbing hills a problem due to how the axle gives into an obstacle instead of pushing into it. The idea is that the more force you push into an obstacle, the better the traction. The less force, the less traction.
As far as better handling, just depends on what flavor you like. Shackle reversals are known for being prone to nosediving when you hit the brakes hard.