I asked an engineer from Easton basically the same question, although with an emphasis on penetration. His reply went something like this.

'Shoot an aluminum arrow at a concrete wall. The arrow will bounce off the wall and land several feet away from the wall. Shoot a carbon arrow with the same mass at the same wall. The carbon arrow will hit the wall and essentially drop down, landing very near the wall.'

The neaning of all that is that the carbon arrow delivered more momentum to the target than the aluminum arrow. The difference being the material of construction. Carbon arrows behave with the properties of carbon, and alluminum arrows behave with the properties of aluminum (imagine that!).