Well, there are advantages and disadvantages of each one.
Du rock is expensive and more difficult to cut. It will not leak and an excellent backing for tile, or whatever.
Green board has been used for a long time. It is special treated drywall that is water resistant, you also need to use water resistant mud and tape also to make the system work. Green board is cheap, but more expensive than reg drywall. Easy to cut and all.
If your on a budget and it is screaming, use Green board,
If you have a shower in the bath, definately use durock in the area around the shower facility, this is for sure. the rest can and could be green board.