Konami has released direct comparison information on the various versions of Ground Zeroes. As you can see, the PS4 is the only version that will run at 1080p resolution; Xbox One has the same resolution as the Xbox 360 and the PS3, although it has the same frame rate as the PS4.
There are a number of very helpful screenshot comparisons as well. Here is a raw image captured from the PS4 during gameplay, and here is an image taken from the Xbox One. You can do more research on this by visiting the compare page of the Ground Zeroes website, like a responsible consumer.