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Since a medium Greatsword does 2d6 and a large one does 3d6 I would be tempted to follow the chart in the monster feat "improved natural attack" which is this:
Improved Natural Attack
Attacks made by one of this creature's natural attacks leave vicious wounds.
Prerequisite: Natural weapon, base attack bonus +4.
Benefit: Choose one of the creature's natural attack forms (not an unarmed strike). The damage for this natural attack increases by one step on the following list, as if the creature's size had increased by one category. Damage dice increase as follows: 1d2, 1d3, 1d4, 1d6, 1d8, 2d6, 3d6, 4d6, 6d6, 8d6, 12d6.
A weapon or attack that deals 1d10 points of damage increases as follows: 1d10, 2d8, 3d8, 4d8, 6d8, 8d8, 12d8.
Special: This feat can be taken multiple times. Each time it is taken, it applies to a different natural attack.
This would put a huge greatsword @ 4d6. The rest of the chart follows the right pattern.
|Chris Lambertz Digital Products Assistant|