This could be due to the PS4 Pro version being released with higher resolution textures.
It has been rumored that the Xbox One version of Call of Duty: WW2 will take up about 45 GB of storage. It comes as a surprise then that the PS4 version of the game will reportedly take up to 80 GB of space.
One explanation could be that the PS4 version of the game is Pro ready so it comes along with 4K textures while this is not the case with the Xbox One version. If Call of Duty WWII supports the Xbox One X, we can expect to see a bump in the game’s size for that version as well. In this case, the 4K texture pack will be automatically downloaded for the Xbox One X version of the game while those playing on the Xbox One will not receive an automatic update.
This is the first game since Call of Duty: World at War that uses the Second World War as its setting. The campaign will follow the stories of the U.S. first infantry as they try to push back Nazis from Europe. Call of Duty:WW2 is set to release on November 3rd for the PS4, Xbox One and PC.