The PlayStation 4 and Xbox One version of Call of Duty: Advanced Warfare are largely the same, but the framerate and resolution are handled in two different ways.
Destiny Sequel Already In Development
Eurogamer's Digital Foundry examined both versions to determine how each console runs the new title, and the results vary depending on what part of the game you're playing. During action-heavy sequences, the PS4 opts to maintain a 1080p resolution at all times by dropping the frames per second from an otherwise constant 60, while the Xbox One will downgrade resolution to maintain 60 frames.
"After a spell in development lingering at 882p and 900p pixel-counts, it's now confirmed that the Xbox One version of Call of Duty: Advanced Warfare uses a dynamic scaling model - rendering at resolutions between 1360x1080 to the full 1920x1080, depending on the intensity of the in-game action," the analysis states.
Grand Theft Auto 5 For PS4, Xbox One And PC Will Have A Full First Person Mode
The PS4 version looks clearer in still images with its constant 1080p (which Xbox One does reach during quiet moments), but with the post-processing effects and motion blur active, the resolution difference is not as obvious in action. Where the PS4 does concede is its framerate--something more noticeable that players will likely care more about.
"From the handling of shadow rendering to texture detail, there's little to distinguish the Xbox One release from the PS4. But based on the first three campaign levels we've analyzed in-depth, the larger disparity is in performance rather than in-game visuals.
"With patch version 1.04 installed, the PS4 version's constant 1080p output comes at a price. We catch dips between the 50-60fps lines during battles through Seoul's streets - with drops to the high 40s caught when throwing the 'threat' grenades to scan the area for enemies. Even in perfectly matched scenes, the Xbox One's performance tends to hold at a perfect 60fps by comparison."
So there you have it, potential Advanced Warfare players. If you're lucky enough to own consoles, there's a choice ahead of you (unless you simply don't care, or have other considerations like what platforms your friends play on) depending on whether you value the higher resolution or consistent FPS. I'd favor the Xbox One framerate as it's likely more noticeable and can affect how you'll play, while the PS4 version might look a bit nicer at times, but the choice is yours.