Speaking completely logical, it would half my strength bonus... and logically, swords have no innate "base attack". Additionally, dual wield styles are exceptionally weak to heavier armor, as yoau have no way to put in the strength in one blow to pierce the enemies armor, or at least have a time with it.
And do not forget what I mentioned: Leverage. Ever looked at a katana or Claymore? Their hilts are very long... this allows you to utilize leverage - this means: You do not just have double the strength, but rather three or four times as much. Leverage is a powerful tool in sword-fighting.
You see, there is a lot of power dual-wield passes on for the sake of versatility.