Is playing a FPS with lower resolution beneficial?
Solution 1:
Most first person shooter engines have a fixed FOV (Field Of View) angle. That means the screen from left to right always shows the same content regardless of screen resolution (usually about 90°).
So a lower resolution on a screen of the same size means basically one thing: larger pixels. Larger pixels mean less detail. That means on long range, a player with a higher resolution can perceive details which a player with a smaller resolution wouldn't. This gives him a distinct gameplay advantage on larger distances.
Also note that running a screen on a different resolution than what it was designed for will result in interpolated pixels which further reduces image quality which can also affect the players performance negatively.
An argument I read in a similar discussion several years ago is that bigger pixels means that you aim at larger targets and thus have an advantage. This is based on the wrong assumption that you hit what you see. This is wrong because hit detection is usually done with invisible hitboxes which aren't affected by the screen resolution of the player. In online gaming it's double-wrong, because the hit detection is done on the server, and the server doesn't even know the resolution the players are playing with.
Solution 2:
The only real reason to reduce resolution is to improve performance. A better solution is to upgrade your computer or reduce other settings in a way to balance smoothness (ideally you want 60 FPS, 20FPS is very bad, 30 FPS is passable but not good) and looks okay.
Higher resolution allows you to see much, much more detail (remember a resolution 2x as wide is actually 4x as many pixels). There's no "stretching the same amount of content" or anything as long as you're in full-screen mode. An object that is 1" wide on a 20", 480p display will be 1" wide on a 20" 1080p display. The only time "stretching" occurs is when you're in windowed mode and the window isn't taking up the full screen area.
There's basically no good non-performance reason to play at a lower resolution.
Additionally some people prefer to play some games at lower resolution since your mouse moves around the screen faster. This doesn't affect FPS games anyway due to how they accept mouse movements, but the proper way to fix that problem is to increase mouse sensitivity and/or DPI.
Solution 3:
As other said, mostly NO, BUT Some older singleplayer games used pixel precision aiming, it can be decided quickly by rendering everything black and only targets colored and ask color of pixel and its player friendly (if you see you should hit, you hit).
As sidenote: there can be benefit of using lesser graphical fidelity. Eg, no flare efects - you are not blinded by light, simple smoke in CS allowed to see through but better obscured much more.
And there can be small advantage in smaller resolution - if some texts are sized in pixels, they can be easier to read when pixels are bigger (but thats beneficial only with smaller native resolution). But that is not something that should have impact on player's performance in FPS (only on comfort)
Solution 4:
If both resolutions run with the same FPS, then setup 1 would be more beneficial. Because it has higher detail and the game will run just as smooth as setup 2.
But because it usually doesn't work that way, if setup 1 gives you 20fps, setup 2 might give you 30 fps. Then setup 2 would be better certainly in a fast action first person shooter.
Frame rates in video games refer to the speed at which the image is refreshed (typically in frames per second, or FPS). Many underlying processes, such as collision detection and network processing, run at different or inconsistent frequencies or in different physical components of a computer. FPS affect the experience in two ways: low FPS does not give the illusion of motion effectively and affects the user's capacity to interact with the game, while FPS that vary substantially from one second to the next depending on computational load produce uneven, “choppy” movement or animation. Many games lock their frame rate at lower but more sustainable levels to give consistently smooth motion.
In modern action-oriented games where players must visually track animated objects and react quickly, frame rates of between 30 and 60 FPS are considered acceptable by most, though this can vary significantly from game to game.
Gotten from : http://en.wikipedia.org/wiki/Frame_rate