Common mode is used for noise where both leads are "bouncing". This noise cannot be removed by capacitive filtering between the wires. You want differential mode, because there is a difference of AC voltage developed between the wires.
Common mode is used where e.g. HF noise must be attenuated, but in particular, differential mode cannot be attenuated. A good example is a switching power supply where HF noise would otherwise feed back into the power line and cause RFI, while the 60Hz power, which would be attenuated, if mildly, in an ordinary LPF, cancels itself out (by the arrangement of the inductors) and passes unscathed.