(1) It's because the longer one is less stiff torsionally. Torque applied at the engine end is resisted by the torque at the wheel end, but sudden application of more engine torque winds the shaft up slightly (like a rubber band), driving the car sideways.
Or...
(2) Basically, it is to do with the different angles that the driveshafts make with the horizontal. When they accelerate, they gain rotational momentum, and if they are at different angles, then there is a net force... it is very strange.