We know by Newton's laws of motion that the reactionary force (F) experinced by a falling body is related with change in momentum (∆p) occurred during the time of change in momentum (∆t) as follows F =∆p/∆t.
Here in both the cases change in momentums (∆p) due to impact are same. But duration of change in momentum (∆t) is more in case of cushioned pillow. So egg experinces less reactionary force and does not break when falls on cushioned pillow.