Two handed weapons such as Greatswords wielded by HG's, do not count as two-handed for the 1.5 Strength damage bonus like it works for regular characters. Basically it's just like having a Human wielding just a Longsword.
The neat feature is that you can wield a Greatsword and a Bastard sword, and the penalties applied for dual-wielding are the same as if you were a Human wielding a Longsword and a Shortsword.

I tested this using the DM-client, possessing several different creatures and checking out the bonuses, there might be a difference on Layo, but if so, i can' tell
