The trailer provided by Kojima productions to compare the different versions of Metal Gear Solid V: Ground Zeroes doesn't do a very good job at actually comparing PS4 and Xbox One, showing them just side by side or in sequence. This screenshot comparison helps seeing the difference a lot better.
Updated with news about why the PS4 version shows no clouds. It is the only one that has a dynamic atmospheric simulation, so the clip was taken when there were no clouds in the sky. But it *will* have clouds.