Question on the Double Bridle.

Hello All,
When useing the Full Bridle in a two hand hold why do most riders use the Austro-Hungarian (German) hold ( curb and snaffle reins crossed)? Can the bits be used independently of one another when held in this fashion?In the Fillis (French)two hand hold there is good separation between the hold on the two bits and I can understand how each can be used separately,together,or on each side of the mouth,one independent of the other.
My regards,
Sandy.