Outside of the candy-coating that makes a game look pretty, and the frame-rate that makes a game appear to run smoothly, resolution can actually have a dramatic impact on game-play itself. Consider that what we're talking about is representing 3d objects with pixels. The lower the resolution, the less pixels to represent an object.
This isn't likely to cause any major imbalance on a console (per say), but on PC it can make a huge difference. For example: I remember making this discovery back when Battlefield 2142 had just come out. My rig at the time could only run the game on low settings at 800x600 resolution. I would get frustrated by how often I would be killed by long-range fire from a distance that I couldn't even see on my own screen. A year passed, I saved up and built a brand new rig that could run the game on max settings at 1280x1024. Suddenly, I was able to see enemies from much farther away, and I was able to take shots at these guys as well now that I could see they were there.
So, the point being... resolution does make a difference. It's the difference between a very distant enemy being rendered with 4 pixels, or none at all. *Essentially a 66% difference between 1080p and 720p. This doesn't have to be an issue, however. So long as the developers are aware of the fixed resolution they will use, and the fixed FOV (or FOV range). Then they can tailor their LOD settings, and projectile ranges to accommodate for fair play conditions.
Being a former COD modder for several years in the past, I can almost guarantee they didn't think of that though. As tomc100 said, they've been using the same exact outdated Quake Engine for years (They've also been using most of the exact same textures, models, and sound effects, too). When a new COD game comes out, it's usually just a subtle mod of the previous one with new level designs, characters, Ui, some hacky new functions, and occasionally new weapons. The core stays nearly exactly the same.
Knowing this, and knowing that all previous COD weapons were capped at a range of 1080 units (roughly 3,542 feet) I would actually be more concerned for the people buying the 1080p version. Every previous COD was made for a lower resolution, and, considering their track-record for oversights and laziness, I wouldn't be surprised if they were still using that same range limit, despite the increase in resolution that would make far away units more visible. In other words, I wouldn't be surprised if PS4 players felt more frustrated trying to hit distant targets.
Anyway... geek-mode deactivated. I hope that made some sense. All that brought back some fond memories and now I feel like coding. Adios!
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