Josh and Speedo, your both kinda right in the wrong ways;
In suspension, oil absorbs energy and springs store it. Heavier oil will absorb more (slowing or controlling the motion) and will not release it afterwards, not in motion anyway. Stiffer springs will store more and it will be release afterwards. The way the oil absorbs (dampens) is the same in compression or rebound if the piston is symmetrical which you can safely assume that it is. I know it does not 'feel' that way to you but it is so.
Heavier oil absorbs more energy but it is also more difficult to transfer it from the wheel (inertia) so it stays longer in the tires on compression.
How all this affects the handling of the car is not always so clear.
...if only I knew why my car barrel rolls...