In a shower area, cement board (cbu) is now the national code (may not be adopted locally, though). Greenboard used to be acceptable, but was not a great choice.
You've got several choices - remove both and install cbu, or leave what is there and cover with a waterproof membrane such as Kerdi from www.schluter.com. Pay particular attension to the edge by the rim of the tub...if the drywall touches the tub, it will swell and fail plus it will degrade with mold.
For guidance on tiling questions, suggest www.johnbridge.com.